grid sweep attempts to parse arg_dict if its not a dict.

.gitmodules

@@ -1,3 +1,15 @@
 [submodule "paper"]
 	path = paper
 	url = git@github.com:chainsawriot/measure.git
+[submodule "overleaf"]
+	path = overleaf
+	url = https://git.overleaf.com/62a956eb9b9254783cc84c82
+[submodule "misclassificationmodels"]
+	path = misclassificationmodels
+	url = https://github.com/chainsawriot/misclassificationmodels.git
+[submodule "presentation"]
+	path = presentation
+	url = https://git.overleaf.com/646be7922a7fb19bcb461593
+[submodule "pyRembr"]
+	path = pyRembr
+	url = git@github.com:groceryheist/pyRembr.git

civil_comments/03_prob_not_pred.R

@@ -0,0 +1,21 @@
+source('load_perspective_data.R')
+source("../simulations/RemembR/R/RemembeR.R")
+library(xtable)
+change.remember.file("prob_not_pred.RDS")
+### to respond to the reviewer show what happens if we don't recode the predictions.
+
+non_recoded_dv <- lm(toxicity_prob ~ likes * race_disclosed, data=df)
+remember(coef(non_recoded_dv), "coef_dv")
+remember(diag(vcov(non_recoded_dv)), "se_dv")
+remember(xtable(non_recoded_dv),'dv_xtable')
+
+non_recoded_iv <- glm(race_disclosed ~ likes * toxicity_prob, data=df, family='binomial')
+remember(coef(non_recoded_iv), "coef_iv")
+remember(diag(vcov(non_recoded_iv)), "se_iv")
+remember(xtable(non_recoded_iv),'iv_xtable')
+
+remember(extract(non_recoded_iv,include.aic=F,include.bic=F,include.nobs=F,include.deviance=F,include.loglik=F),'non_recoded_iv')
+remember(extract(non_recoded_dv,include.rsquared=F,include.adjrs=F,include.nobs=F),'non_recoded_dv')
+tr <- texreg(list(r$non_recoded_iv, r$non_recoded_dv),custom.model.names=c("Example 1","Example 2"),custom.coef.map=list("(Intercept)"="Intercept","race_disclosedTRUE"="Identity Disclosure","toxicity_prob"="Toxicity Score","likes"="Likes","likes:race_disclosedTRUE"="Likes:Identity Disclosure","likes:toxicity_prob"="Likes:Toxicity Score"),single.row=T,dcolumn=T)
+print(tr)
+remember(tr, 'texregobj')

civil_comments/Makefile

@@ -1,4 +1,4 @@
-qall: iv_perspective_example.RDS dv_perspective_example.RDS
+all: iv_perspective_example.RDS dv_perspective_example.RDS
 
 srun_1core=srun -A comdata -p compute-bigmem --mem=4G --time=12:00:00 -c 1 --pty /usr/bin/bash -l
 srun=srun -A comdata -p compute-bigmem --mem=4G --time=12:00:00 --pty /usr/bin/bash -l

multiple_iv_simulations/01_indep_differential.R

@@ -0,0 +1,132 @@
+library(argparser)
+library(mecor)
+library(ggplot2)
+library(data.table)
+library(filelock)
+library(arrow)
+library(Amelia)
+library(Zelig)
+library(predictionError)
+options(amelia.parallel="no",
+        amelia.ncpus=1)
+setDTthreads(40)
+
+source("simulation_base.R")
+
+simulate_data <- function(N,
+                          m,
+                          B0,
+                          Bxy,
+                          Bzx,
+                          Bzy,
+                          seed,
+                          y_explained_variance = 0.025,
+                          prediction_accuracy = 0.73,
+                          y_bias = -0.8,
+                          z_bias = 0,
+                          x_bias = 0,
+                          Px = 0.5,
+                          Pz = 0.5,
+                          accuracy_imbalance_difference = 0.3) {
+  set.seed(seed)
+  # make w and y dependent
+  z <- rbinom(N, 1, plogis(qlogis(Pz)))
+  x <- rbinom(N, 1, plogis(Bzx * z + qlogis(Px)))
+
+  y.var.epsilon <- (var(Bzy * z) + var(Bxy * x) + 2 * cov(Bzy * z, Bxy * x)) * ((1 - y_explained_variance) / y_explained_variance)
+  y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
+  y <- Bzy * z + Bxy * x + y.epsilon
+
+  df <- data.table(x = x, y = y, z = z)
+
+  if (m < N) {
+    df <- df[sample(nrow(df), m), ":="(x.obs = x, z.obs = z)]
+  } else {
+    df <- df[, ":="(x.obs = x, z.obs = z)]
+  }
+
+  resids <- resid(lm(y ~ x + z))
+  odds.x1 <- qlogis(prediction_accuracy) + y_bias * qlogis(pnorm(resids[x == 1])) + z_bias * qlogis(pnorm(z[x == 1], sd(z)))
+  odds.x0 <- qlogis(prediction_accuracy, lower.tail = F) + y_bias * qlogis(pnorm(resids[x == 0])) + z_bias * qlogis(pnorm(z[x == 0], sd(z)))
+
+  ## acc.x0 <- p.correct[df[,x==0]]
+  ## acc.x1 <- p.correct[df[,x==1]]
+
+  df[x == 0, w := plogis(rlogis(.N, odds.x0))]
+  df[x == 1, w := plogis(rlogis(.N, odds.x1))]
+  df[, w_pred := as.integer(w > 0.5)]
+
+  ## now let's use another classifier for z
+  odds.z1 <- qlogis(prediction_accuracy) + y_bias * qlogis(pnorm(resids[z == 1])) + x_bias * qlogis(pnorm(x[z == 1], sd(x)))
+  odds.z0 <- qlogis(prediction_accuracy, lower.tail = F) + y_bias * qlogis(pnorm(resids[z == 0])) + x_bias * qlogis(pnorm(x[z == 0], sd(z)))
+
+  df[z == 0, a := plogis(rlogis(.N, odds.z0))]
+  df[z == 1, a := plogis(rlogis(.N, odds.z1))]
+  df[, a_pred := as.integer(a > 0.5)]
+
+
+  print(mean(df$w_pred == df$x))
+  print(mean(df$w_pred == df$x))
+  print(mean(df[y >= 0]$w_pred == df[y >= 0]$x))
+  print(mean(df[y <= 0]$w_pred == df[y <= 0]$x))
+  return(df)
+}
+
+parser <- arg_parser("Simulate data and fit corrected models with two independent variables that are classified")
+parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
+parser <- add_argument(parser, "--seed", default=51, help='seed for the rng')
+parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.1)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.75)
+parser <- add_argument(parser, "--accuracy_imbalance_difference", help='how much more accurate is the predictive model for one class than the other?', default=0.3)
+parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=0.3)
+parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
+parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y*z*x")
+parser <- add_argument(parser, "--y_bias", help='coefficient of y on the probability a classification is correct', default=-0.5)
+parser <- add_argument(parser, "--z_bias", help='coefficient of z on the probability a classification is correct', default=0)
+parser <- add_argument(parser, "--x_bias", help='coefficient of x on the probability a classification is correct', default=0)
+parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
+parser <- add_argument(parser, "--Px", help='base rate of x', default=0.5)
+parser <- add_argument(parser, "--confint_method", help='method for approximating confidence intervals', default='quad')
+args <- parse_args(parser)
+
+B0 <- 0
+Px <- args$Px
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+Bzx <- args$Bzx
+
+if(args$m < args$N){
+
+    df <- simulate_data(args$N, args$m, B0, Bxy, Bzx, Bzy, args$seed, args$y_explained_variance, args$prediction_accuracy, y_bias=args$y_bias)
+
+    ## df.pc <- df[,.(x,y,z,w_pred,w)]
+    ##                                     #    df.pc <- df.pc[,err:=x-w_pred]
+    ## pc.df <- pc(suffStat=list(C=cor(df.pc),n=nrow(df.pc)),indepTest=gaussCItest,labels=names(df.pc),alpha=0.05)
+    ## plot(pc.df)
+
+    result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, 'Bzx'=args$Bzx, 'Bzy'=Bzy, 'Px'=Px, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, 'y_bias'=args$y_bias,'outcome_formula'=args$outcome_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, confint_method=args$confint_method, error='')
+
+  research_data <- df[is.na(x.obs), .(w = w_pred, a = a_pred, y = y)] |> as.data.frame()
+
+  val_data <- df[!is.na(x.obs), .(w = w_pred, a = a_pred, z = z.obs, y = y, x = x.obs)] |> as.data.frame()
+
+  outline <- run_simulation(y ~ x || w + z ||
+    a, w ~ x + z + y, a ~ x + z + y, data=research_data,data2=val_data, result = result)
+    
+   
+ outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+    if(file.exists(args$outfile)){
+        logdata <- read_feather(args$outfile)
+        logdata <- rbind(logdata,as.data.table(outline), fill=TRUE)
+    } else {
+        logdata <- as.data.table(outline)
+    }
+
+    print(outline)
+    write_feather(logdata, args$outfile)
+    unlock(outfile_lock)
+}

multiple_iv_simulations/Makefile

@@ -0,0 +1,41 @@
+.ONESHELL:
+SHELL=bash
+
+Ns=[1000, 5000, 10000]
+ms=[100, 200, 400]
+seeds=[$(shell seq -s, 1 500)]
+explained_variances=[0.1]
+
+all:main
+main:remembr.RDS 
+
+srun=sbatch --wait --verbose skx_1.sbatch
+skx_pylauncher_limit=40
+
+joblists:example_1_jobs example_2_jobs example_3_jobs
+
+grid_sweep_script=../simulations/grid_sweep.py 
+
+example_1_jobs: 01_indep_differential.R simulation_base.R ${grid_sweep_script} skx_1.sbatch ../misclassificationmodels
+	${srun} uv run ${grid_sweep_script} --command "Rscript 01_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_1.feather"], "y_explained_variance":${explained_variances}, "Bzx":[1]}' --outfile example_1_jobs
+
+example_1.feather: example_1_jobs my_pylauncher.py
+	sbatch -J "multiple iv measerr correction" skx_1.sbatch my_pylauncher.py $< --cores 1
+
+remembr.RDS:example_1.feather 
+# 	rm -f remembr.RDS
+# 	${srun} Rscript plot_example.R --infile example_1.feather --name "plot.df.example.1"
+
+
+clean_main:
+	rm -f example_1_jobs
+	rm -f example_1.feather
+#	
+clean_all: clean_main
+	rm *.feather
+	rm -f remembr.RDS
+	rm -f remembr*.RDS
+	rm -f robustness*.RDS
+	rm -f example_*_jobs
+	rm -f robustness_*_jobs_*
+

multiple_iv_simulations/my_pylauncher.py

@@ -0,0 +1,18 @@
+#!/scratch/projects/compilers/intel24.0/oneapi/intelpython/python3.9/bin/python3
+#^ always use TACC's python to start pylauncher. 
+
+import pylauncher 
+import argparse
+import sys
+
+parser = argparse.ArgumentParser()
+parser.add_argument('jobs', help='list of commands to be run')
+parser.add_argument('--cores', help='cores to use per job', default=1)
+parser.add_argument('--timeout', help='timeout length (seconds)', default=2)
+parser.add_argument('--queuestate', help='pylauncher queuestate (for resuming jobs)',default=None)
+
+args = parser.parse_args()
+if args.queuestate is not None:
+    pylauncher.ResumeClassicLauncher(args.queuestate, cores=args.cores, timeout=args.timeout)
+else:
+    pylauncher.ClassicLauncher(args.jobs, cores=args.cores, timeout=args.timeout)

multiple_iv_simulations/pyproject.toml

@@ -0,0 +1,22 @@
+[project]
+name = "multiple-iv-simulations"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+requires-python = ">=3.11"
+dependencies = [
+    "fire>=0.7.0",
+    "numpy>=2.2.6",
+    "pandas>=2.3.0",
+    "pylauncher>=4.0",
+    "pyremember>=0.2.0",
+    "rpy2>=3.6.0",
+]
+
+[tool.uv.sources]
+pyremember = { git = "https://github.com/groceryheist/pyRembr" }
+
+[dependency-groups]
+dev = [
+    "pytest>=8.4.0",
+]

multiple_iv_simulations/simulation_base.R

@@ -0,0 +1,118 @@
+options(amelia.parallel="no",
+        amelia.ncpus=1)
+library(matrixStats) # for numerically stable logsumexps
+source("../misclassificationmodels/R/likelihoods.R")
+source("../misclassificationmodels/R/glm_fixit.R")
+
+## ... are the parts of the formular.
+run_simulation <-  function(..., family=gaussian(),
+                      proxy_family = binomial(link='logit'),
+                      truth_family = binomial(link='logit'),
+                      data,
+                      data2,
+                      result
+                      ){
+
+    accuracy <- df[,mean(w_pred==x)]
+    accuracy.x.y0 <- df[y<=0,mean(w_pred==x)]
+    accuracy.x.y1 <- df[y>=0,mean(w_pred==x)]
+    accuracy.z.y0 <- df[y<=0,mean(a_pred==z)]
+    accuracy.z.y1 <- df[y>=0,mean(a_pred==z)]
+    cor.y.xi <- cor(df$x - df$w_pred, df$y)
+    cor.y.zi <- cor(df$z - df$a_pred, df$y)
+
+    fnr <- df[w_pred==0,mean(w_pred!=x)]
+    fnr.y0 <- df[(w_pred==0) & (y<=0),mean(w_pred!=x)]
+    fnr.y1 <- df[(w_pred==0) & (y>=0),mean(w_pred!=x)]
+
+    fpr <- df[w_pred==1,mean(w_pred!=x)]
+    fpr.y0 <- df[(w_pred==1) & (y<=0),mean(w_pred!=x)]
+    fpr.y1 <- df[(w_pred==1) & (y>=0),mean(w_pred!=x)]
+    cor.resid.w_pred <- cor(resid(lm(y~x+z,df)),df$w_pred)
+
+    result <- append(result, list(accuracy=accuracy,
+                                  accuracy.x.y0=accuracy.x.y0,
+                                  accuracy.x.y1=accuracy.x.y1,
+                                  accuracy.z.y0=accuracy.z.y0,
+                                  accuracy.z.y1=accuracy.z.y1,
+                                  cor.y.xi=cor.y.xi,
+                                  fnr=fnr,
+                                  fnr.y0=fnr.y0,
+                                  fnr.y1=fnr.y1,
+                                  fpr=fpr,
+                                  fpr.y0=fpr.y0,
+                                  fpr.y1=fpr.y1,
+                                  cor.resid.w_pred=cor.resid.w_pred
+                                  ))
+
+    result <- append(result, list(cor.xz=cor(df$x,df$z)))
+    (model.true <- lm(y ~ x + z, data=df))
+    true.ci.Bxy <- confint(model.true)['x',]
+    true.ci.Bzy <- confint(model.true)['z',]
+
+    result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
+                                  Bzy.est.true=coef(model.true)['z'],
+                                  Bxy.ci.upper.true = true.ci.Bxy[2],
+                                  Bxy.ci.lower.true = true.ci.Bxy[1],
+                                  Bzy.ci.upper.true = true.ci.Bzy[2],
+                                  Bzy.ci.lower.true = true.ci.Bzy[1]))
+                                  
+  ## mle_result <- list(
+  ##   Bxy.est.naive = NULL,
+  ##   Bxy.ci.upper.naive = NULL,
+  ##   Bxy.ci.lower.naive = NULL,
+  ##   Bzy.est.naive = NULL,
+  ##   Bzy.ci.upper.naive = NULL,
+  ##   Bzy.ci.lower.naive = NULL,
+  ##   Bxy.est.feasible = NULL,
+  ##   Bxy.ci.upper.feasible = NULL,
+  ##   Bxy.ci.lower.feasible = NULL,
+  ##   Bzy.est.feasible = NULL,
+  ##   Bzy.ci.upper.feasible = NULL,
+  ##   Bzy.ci.lower.feasible = NULL,
+  ##   Bxy.est.mle = NULL,
+  ##   Bxy.ci.upper.mle = NULL,
+  ##   Bxy.ci.lower.mle = NULL,
+  ##   Bzy.est.mle = NULL,
+  ##   Bzy.ci.upper.mle = NULL,
+  ##   Bzy.ci.lower.mle = NULL
+  ## )
+  ## tryCatch({
+    mod <- glm_fixit(..., family=family, data=data, data2=data2)
+  
+    coef_corrected <- coef(mod, which_model = "corrected")
+    ci_corrected <- confint(mod, which_model = "corrected")
+    
+    coef_feasible <- coef(mod, which_model = "feasible")
+    ci_feasible <- confint(mod, which_model = "feasible")
+    
+    coef_naive <- coef(mod, which_model = "naive")
+    ci_naive <- confint(mod, which_model = "naive")
+    
+    mle_result <- list(
+      Bxy.est.mle = coef_corrected["x"],
+      Bxy.ci.upper.mle = ci_corrected["x", 2],
+      Bxy.ci.lower.mle = ci_corrected["x", 1],
+      Bzy.est.mle = coef_corrected["z"],
+      Bzy.ci.upper.mle = ci_corrected["z", 2],
+      Bzy.ci.lower.mle = ci_corrected["z", 1],
+      Bxy.est.feasible = coef_feasible["x"],
+      Bxy.ci.upper.feasible = ci_feasible["x", 2],
+      Bxy.ci.lower.feasible = ci_feasible["x",1],
+      Bzy.est.feasible = coef_feasible["z"],
+      Bzy.ci.upper.feasible = ci_feasible["z",2],
+      Bzy.ci.lower.feasible = ci_feasible["z",1],
+      Bxy.est.naive = coef_naive["w"],
+      Bxy.ci.upper.naive = ci_naive["w",2],
+      Bxy.ci.lower.naive = ci_naive["w",1],
+      Bzy.est.naive = coef_naive["a"],
+      Bzy.ci.upper.naive = ci_naive["a",2],
+      Bzy.ci.lower.naive = ci_naive["a",1]
+    )
+  ##     print(mle_result)
+  ## },
+  ## error=function(e) {result[['error']] <- as.character(e)
+  ## })
+  result <- append(result, mle_result)
+  return(result)
+}

multiple_iv_simulations/skx_1.sbatch

@@ -0,0 +1,12 @@
+#!/bin/bash
+#SBATCH --account=ECS24013
+#SBATCH --partition=skx
+#SBATCH --nodes=1
+#SBATCH --chdir=/scratch/10114/nathante/critical_mass
+#SBATCH --error="sbatch_log/%x_%A_%a.err"
+#SBATCH --output="sbatch_log/%x_%A_%a.out"
+#SBATCH --nice
+#SBATCH --time=48:00:00
+
+source ~/.bashrc
+"$@"

presentations/ica_hackathon_2022/.Rhistory

@@ -1,291 +0,0 @@
-ls()
-weight
-weight
-lablr
-labelr
-nrow(labelr)
-names(labelr)
-names(labelr$data)
-labelr$data
-labelr
-names(labelr)
-labelr$labelr
-labelr$toxic
-setwd("..")
-q()
-n
-summary(toxicity_calibrated)
-qplot(labelr$toxic,type='hist')
-names(labelr)
-labelr$n
-labelr
-names(labelr)
-fbyg
-gghist(fbyg$weight)
-hist(fbyg$weight)
-hist(log(fbyg$weight))
-fbyg$weight==1
-all(fbyg$weight==1)
-fbyg$weight[fbyg$weight != 1]
-fbyg[fbyg$weight != 1]
-fbyg[,fbyg$weight != 1]
-fbyg[[fbyg$weight != 1]]
-fbyg[fbyg$weight != 1,]
-names(labelr)
-summary(toxicity_calibrated)
-toxicity_calibrated
-val.data
-names(labelr)
-labelr$data
-labelr
-labelr[data]
-labelr[data=='yg']
-labelr[,data=='yg']
-labelr[data=='yg',]
-labelr[labelr$data=='yg']
-labelr[,labelr$data=='yg']
-labelr[labelr$data=='yg',]
-toxicity_calibrated
-summary(toxicity_calibrated)
-yg3
-yg3[,['toxic','toxic_pred']]
-yg3 %>% select('toxic','toxic_pred')
-yg3 |> select('toxic','toxic_pred')
-names(yg3)
-yg3[,c('toxic_pred','toxic')]
-corr(yg3[,c('toxic_pred','toxic')])
-cor(yg3[,c('toxic_pred','toxic')])
-cor(yg3[,c('toxic_pred','toxic')],na.rm=T)
-cor(yg3[,c('toxic_pred','toxic')],rm.na=T)
-?cor(yg3[,c('toxic_pred','toxic')],use=
-?cor
-cor(yg3[,c('toxic_pred','toxic')],use='all.obs')
-?cor
-cor(yg3[,c('toxic_pred','toxic')],use='complete.obs')
-cor(yg3[,c('toxic_pred','toxic')],use='complete.obs',method='spearman')
-?predict
-yg3$toxic_pred
-names(preds)
-preds
-preds
-preds$error
-preds
-preds
-summary(errormod)
-summary(errormod)
-summary(preds)
-names(preds)
-preds
-resids
-qplot(resids)
-resids
-?predict.lm
-dnorm(1)
-dnorm(2)
-dnorm(1)
-pnorm(1)
-preds
-p1 + p2
-p1 + p2
-p1
-p2
-preds
-preds1 <- preds
-preds1$diff - preds$diff
-preds1$diff 
-preds1$diff - preds1$diff
-preds1$diff - preds$diff
-preds1$diff - preds$diff
-preds1$diff - preds$diff
-preds1$diff - preds$diff
-preds1
-preds
-dnorm(-1)
-dnorm(1)
-pnorm(1)
-pnorm(-1)
-pnorm(2)
-pnorm(9)
-pnorm(6)
-pnorm(2)
-dnorm(0.95)
-qnorm(0.95)
-qnorm(0.841)
-fulldata_preds
-names(yg3)
-yg3$toxic_feature_1
-yg3$toxic_feature_2
-yg3
-yg3[,.(toxic_pred,toxic_var)]
-yg3[,.(toxic_pred,toxicity_2_pred_sigma,toxicity_1_pred_sigma)]
-yg3[,.(toxic_pred,toxicity_2_pred_sigma,toxicity_1_pred_sigma,cov(toxicity_2_pred,toxicity_1_pred))]
-cov(1,2)
-cov(c(1),c(3))
-cov(c(1),c(3,2))
-cov(c(1,1),c(3,2))
-cov(c(1,2),c(3,2))
-covterm
-covterm
-?cov
-covterm
-yg3
-yg3[,.(toxic_pred,toxicity_2_pred_sigma,toxicity_1_pred_sigma,cov(toxicity_2_pred,toxicity_1_pred))]
-yg3[,.(toxic_pred,toxicity_2_pred_sigma,toxicity_1_pred_sigma,toxic_var)]
-yg3[,.(toxic_pred,toxicity_2_pred_sigma,toxicity_1_pred_sigma,toxic_var,toxic_sd)]
-yg3
-names(yg3)
-print(sg)
-print(sg)
-1+1
-library(stargazer)
-
-stargazer(w1,w2,w3,w4,w5,t1,t2,t3,t4,t5, type="text",
-          keep = c("cond1","meantox","cond1:meantox","Constant"),
-          keep.stat=c("n","adj.rsq"),
-          model.numbers = F,
-          dep.var.labels = c("DV = Willingness to comment","DV = Toxicity of YG respondent comments"),
-          covariate.labels = c("Treatment (top comments shown)",
-                               "Average toxicity of top comments",
-                               "Treatment $\times$ top comments toxicity",
-                               "Constant"),
-          add.lines = list(c("Article fixed effects","No","No","No","Yes","Yes","No","No","No","Yes","Yes")),
-          star.cutoffs = c(0.05,0.01,0.005),
-          notes = "Standard errors are clustered at the respondent level.",
-          column.labels = c("(1)","(2)","(3)","(4)","(5)","(6)","(7)","(8)","(9)","(10)"),
-          style = "apsr")
-
-q()
-n
-yglabels
-labelr
-names(labelr)
-fb
-names(fb
-)
-fb.comment_id
-fb['comment_id']
-fb[,'comment_id']
-labelr[,'comment_id']
-names(fb)
-fb.labeled
-names(fb.labeled)
-names(yg)
-?amelia
-yg
-names(yg)
-names(yg3)
-?rbind
-nrow(yg3)
-nrow(yg)
-yg3[,.(.N),by=.(toxic,fb)]
-yg3.toimpute
-names(yg3.toimpute)
-yg3.toimpute
-names(yg3.toimpute)
-names(labelr)
-nrow(yg3)
-nrow(labelr)
-?merge.data.table
-labelr
-is.data.table(labelr)
-yg3.toimpute
-overimp.grid
-overimp.grid
-?amelia
-q()
-n
-setwd("presentations/ica_hackathon_2022/")
-ls()
-attach(r)
-example_2_B.plot.df
-library(ggplot2)
-example_2_B.plot.df[(variable=='x') && (m < 1000)]
-example_2_B.plot.df[(variable=='x') && (m < 1000)]
-theme_set(theme_default())
-theme_set(theme_minimal())
-theme_set(theme_classic())
-example_2_B.plot.df[(variable=='x') && (m < 1000)]
-example_2_B.plot.df[(variable=='x') && (m < 1000),unique(method)]
-as.factor
-update.packages()
-update.packages()
-update.packages()
-cancel
-plot.df
-example_2_B.plot.df
-plot.df
-example_2_B.plot.df
-example_2_B.plot.df$method %>% unique
-example_2_B.plot.df$method |> unique
-example_2_B.plot.df$method  |> uniq
-unique(example_2_B.plot.df$method)
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-example_2_B.plot.df <- r$example_2_B.plot.df
-q()
-n
-setwd("presentations/ica_hackathon_2022/')
-setwd("presentations/ica_hackathon_2022/")
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-q()
-n
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-q()
-n
-example_2_B.plot.df$method
-example_2_B.plot.df$method
-q()
-n
-q()
-n
-plot.df
-plot.df
-plot.df[,.N,by=.(N,m)]
-plot.df[,.N,by=.(N,m,method)]
-plot.df[variable=='x',.N,by=.(N,m,method)]
-plot.df
-plot.df[(variable=='x') & (m < 1000) & (!is.na(p.true.in.ci))]
-plot.df[(variable=='x') & (m != 1000) & (!is.na(p.true.in.ci))]
-plot.df
-?label_wrap_gen
-install.packages("ggplot2")
-devtools::install_github("tidyverse/ggplot2")
-2
-library(ggplot2)
-ggplot2::version
-sessioninfo()
-sessionInfo()
-q()
-n
-sessionInfo()
-?scale_x_discrete
-?facet_grid
-plot.df
-plot.df
-plot.df[method="2SLS+gmm"]
-plot.df[method=="2SLS+gmm"]
-df <- example_2_B.plot.df
-df
-q()
-n
-plot.df
-plot.df[m=50]
-plot.df[m==50]
-plot.df.example.2[m==50][method=2SLS+gmm]
-plot.df.example.2[m==50][method==2SLS+gmm]
-plot.df.example.2[(m==50) & (method==2SLS+gmm)]
-plot.df.example.2[(m==50) & (method=="2SLS+gmm")]
-plot.df[m==50]
-plot.df.example.3
-plot.df.example.3
-plot.df.example.3[N=25000]
-plot.df.example.3[N==25000]
-plot.df
-plot.df
-plot.df
-q()
-n

presentations/ica_hackathon_2022/Makefile

@@ -1,26 +0,0 @@
-#!/usr/bin/make
-all:html pdf
-
-html: $(patsubst %.Rmd,%.html,$(wildcard *.Rmd)) 
-pdf: $(patsubst %.Rmd,%.pdf,$(wildcard *.Rmd)) 
-
-remembr.RDS:
-	rsync klone:/gscratch/comdata/users/nathante/ml_measurement_error/mi_simulations/remembr.RDS .
-
-%.pdf:  %.html
-	Rscript -e 'xaringan::decktape("$<","$@",docker=FALSE)'
-
-%.html: %.Rmd *.css remembr.RDS
-	Rscript -e 'library(rmarkdown); rmarkdown::render("$<", output_file = "$@")'
-#	firefox "$@"
-
-clean:
-	rm *.html
-	rm -r *_files
-	rm -r *_cache
-
-publish: all pdf
-	scp -r *.html groc:/home/nathante/public_html/slides/measurement_error_comdatahack_2022.html
-	scp -r *.pdf groc:/home/nathante/public_html/slides/measurement_error_comdatahack_2022.pdf
-
-.PHONY: clean all

presentations/ica_hackathon_2022/ica_hackathon_2022.Rmd

@@ -1,724 +0,0 @@
----
-title: "How good of a model do you need? Accounting for classification errors in machine assisted content analysis."
-author: Nathan TeBlunthuis
-date: May 24 2022
-template: "../resources/template.html"
-output: 
-  xaringan::moon_reader:
-    lib_dir: libs
-    seal: false
-    nature: 
-        highlightStyle: github
-        ratio: 16:9
-        countIncrementalSlides: true
-        slideNumberFormat: |
-          <div class="progress-bar-container">
-            <div class="progress-bar" style="width: calc(%current% / %total% * 100%);">
-            </div>
-          </div>
-    self_contained: false
-    css: [default, my-theme.css, fontawesome.min.css]
-    chakra: libs/remark-latest.min.js
-
----
-```{r echo=FALSE, warning=FALSE, message=FALSE}
-library(knitr)
-library(ggplot2)
-library(data.table)
-library(icons)
-
-f <- function (x) {formatC(x, format="d", big.mark=',')}
-
-theme_set(theme_bw())
-r <- readRDS('remembr.RDS')
-attach(r)
-
-```
-class: center, middle, narrow
-
-<script type='javascript'>
-window.MathJax = {
-  loader: {load: ['[tex]/xcolor']},
-  tex: {packages: {'[+]': ['xcolor']}}
-};
-</script>
-
-<div class="my-header"></div>
-
-
-###  .title-heading[Unlocking the power of big data: The importance of measurement error in machine assisted content analysis]
-## Nathan TeBlunthuis
-
-<img src="images/nu_logo.png" height="170px" style="padding:21px"/> <img src="images/uw_logo.png" height="170px" style="padding:21px"/> <img src="images/cdsc_logo.png" height="170px" style="padding:21px"/>
-
-
-`r icons::fontawesome('envelope')` nathan.teblunthuis@northwestern.edu
-
-`r icons::fontawesome('globe')` [https://teblunthuis.cc](https://teblunthuis.cc)
-
-???
-
-This talk will be me presenting my "lab notebook" and not a polished research talk.  Maybe it would be a good week of a graduate seminar? In sum, machine assisted content analysis has unique limitations and threats to validity that I wanted to understand better.  I've learned how the noise introduced by predictive models can result in misleading statistical inferences, but that a sample of human-labeled validation data can often be used to account for this noise and obtain accurate inferences in the end.  Statistical knowledge of this problem and computational tools for addressing are still in development.  My goals for this presentation are to start sharing this information with the community and hopeful to stimulate us to work on extending existing approaches or using them in our work.
-
-This is going to be a boring talk about some *very* technical material. If you're not that interested please return to your hackathon. Please interrupt me if I'm going too fast for you or if you don't understand something.  I will try to move quickly in the interests of those wishing to wrap up their hackathon projects. I will also ask you to show hands once or twice, if you are already familiar with some concepts that it might be expedient to skip.
-
----
-
-class:center, middle, inverse
-## Machine assistent content analysis (MACA)
-
-???
-
-I'm going to start by defining a study design that is increasingly common, especially in Communication and Political Science, but also across the social sciences and beyond. I call it *machine assisted content analysis* (MACA).
-
----
-<div class="my-header"></div>
-
-### .border[Machine assisted content analysis (MACA) uses machine learning for scientific measurement.]
-
-.emph[Content analysis:] Statistical analysis of variables measured by human labeling ("coding") of content.  This might be simple categorical labels, or maybe more advanced annotations.
-
---
-
-*Downside:* Human labeling is *a lot* of work.
-
---
-
-.emph[Machine assisted content analysis:] Use a *predictive algorithm* (often trained on human-made labels) to measure variables for use in a downstream *primary analysis.*
-
---
-
-*Downside:*  Algorithms can be *biased* and *inaccurate* in ways that could invalidate the statistical analysis.
-
-
-???
-
-A machine assisted content analysis can be part of a more complex or more powerful study design (e.g., an experiment, time series analysis &c). 
-
----
-
-
-<!-- <div class="my-header"></div> -->
-
-<!-- ### .border[Hypothetical Example: Predicting Racial Harassement in Social Media Comments] -->
-
----
-class:large 
-
-<div class="my-header"></div>
-
-### .border[How can MACA go wrong?]
-
-Algorithms can be *biased* and *error prone* (*noisy*).
-
---
-
-Predictor bias is a potentially difficult problem that requires causal inference methods. I'll focus on *noise* for now.
-
---
-
-Noise in the predictive model introduces bias in the primary analysis.
-
---
-
-.indent[We can reduce and sometimes even *eliminate* this bias introduced by noise.]
-
----
-layout:true
-<div class="my-header"></div>
-
-### .border[Example 1: An unbiased, but noisy classifier]
-
-.large[.left-column[![](images/example_1_dag.png)]]
-
-???
-
-Please show hands if you are familiar with causal graphs or baysian networks.  Should I explain what this diagram means?
-
-
----
-
-.right-column[
-$x$ is *partly observed* because we have *validation data* $x^*$.
-]
-
----
-
-
-.right-column[
-$x$ is *partly observed* because we have *validation data* $x^*$.
-
-$k$ are the *features* used by the *predictive model* $g(k)$.
-
-]
-
----
-
-.right-column[
-$x$ is *partly observed* because we have *validation data* $x^*$.
-
-$k$ are the *features* used by the *predictive model* $g(k)$.
-
-The predictions $w$ are a *proxy variable*  $g(k) = \hat{x} = w$.
-
-]
-
----
-
-
-.right-column[
-$x$ is *partly observed* because we have *validation data* $x^*$.
-
-$k$ are the *features* used by the *predictive model* $g(k)$.
-
-The predictions $w$ are a *proxy variable*  $g(k) = \hat{x} = w$.
-
-$x = w + \xi$ because the predictive model makes errors.
-
-]
-
----
-
-
-layout:true
-<div class="my-header"></div>
-
-### .border[Noise in a *covariate* creates *attenuation bias*.]
-
-.large[.left-column[![](images/example_1_dag.png)]]
-
----
-.right-column[
-
-We want to estimate, $y = Bx + \varepsilon$, but we estimate $y = Bw + \varepsilon$ instead.
-
-$x = w + \xi$ because the predictive model makes errors.
- 
-]
----
-
-.right-column[
-
-We want to estimate, $y = Bx + \varepsilon$, but we estimate $y = Bw + \varepsilon$ instead.
-
-$x = w + \xi$ because the predictive model makes errors.
-
- 
-Assume $g(k)$ is *unbiased* so $E(\xi)=0$. Also assume error is *nondifferential* so $E(\xi y)=0$:
-
-]
-
----
-
-.right-column[
-
-We want to estimate, $y = Bx + \varepsilon$, but we estimate $y = Bw + \varepsilon$ instead.
-
-$x = w + \xi$ because the predictive model makes errors.
-
-Assume $g(k)$ is *unbiased* so $E(\xi)=0$. Also assume error is *nondifferential* so $E(\xi y)=0$:
-
-$$\widehat{B_w}^{ols}=\frac{\sum^n_{j=j}{(x_j + \xi_j - \overline{(x + \xi)})}(y_j - \bar{y})}{\sum_{j=1}^n{(x_j + \xi_j - \overline{(x+\xi)})^2}} = \frac{\sum^n_{j=j}{(x_j - \bar{x})(y_j -
- \bar{y})}}{\sum_{j=1}^n{(x_j + \xi_j - \bar{x}){^2}}}$$
-
-]
-
----
-
-.right-column[
-
-We want to estimate, $y = Bx + \varepsilon$, but we estimate $y = Bw + \varepsilon$ instead.
-
-$x = w + \xi$ because the predictive model makes errors.
-
-Assume $g(k)$ is *unbiased* so $E(\xi)=0$. Also assume error is *nondifferential* so $E(\xi y)=0$:
-
-$$\widehat{B_w}^{ols}=\frac{\sum^n_{j=j}{(x_j + \xi_j - \overline{(x + \xi)})}(y_j - \bar{y})}{\sum_{j=1}^n{(x_j + \xi_j - \overline{(x+\xi)})^2}} = \frac{\sum^n_{j=j}{(x_j - \bar{x})(y_j -
- \bar{y})}}{\sum_{j=1}^n{(x_j + \color{red}{\xi_j} - \bar{x})\color{red}{^2}}}$$
-
-In this scenario, it's clear that $\widehat{B_w}^{ols} < B_x$.
-
-
-]
-
-
-???
-
-Please raise your hands if you're familiar with attenuation bias.  I expect that its covered in some graduate stats classes, but not universally.
-
----
-class:large
-layout:false
-<div class="my-header"></div>
-
-### .border[Beyond attenuation bias]
-.larger[Measurement error can theaten validity because:]
-
-- Attenuation bias *spreads* (e.g., to marginal effects as illustrated later).
-
---
-
-- Measurement error can be *differential*— not distributed evenly and possible correlated with $x$, $y$, or $\varepsilon$.
-
---
-
-- *Bias can be away from 0* in GLMs and nonlinear models or if measurement error is differential.
-
---
-
-- *Confounding* if the *predictive model is biased* introducing a correlation the measurement error and the residuals $(E[\xi\varepsilon]=0)$. 
-
-
----
-
-class:large
-layout:false
-<div class="my-header"></div>
-
-### .border[Correcting measurement error]
-
-There's a vast literature in statistics on measurement error. Mostly about noise you'd find in sensors. Lots of ideas. No magic bullets.
-
---
-
-I'm going to briefly cover 3 different approaches: *multiple imputation*,  *regression calibration* and *2SLS+GMM*.
-
---
-
-These all depend on *validation data*. I'm going to ignore where this comes from, but assume it's a random sample of the hypothesis testing dataset. 
-
---
-
-You can *and should* use it to improve your statistical estimates. 
-
----
-
-<div class="my-header"></div>
-
-### .border[Multiple Imputation (MI) treats Measurement Error as a Missing Data Problem]
-
-1. Use validation data to estimate $f(x|w,y)$, a probabilistic model of $x$.
-
---
-
-2. *Sample* $m$ datasets from $\widehat{f(x|w,y)}$.
-
---
-
-3. Run your analysis on each of the $m$ datasets.
-
---
-
-4. Average the results from the $m$ analyses using Rubin's rules.
-
---
-
-.e[Advantages:] *Very flexible!* Sometimes can work if the predictor $g(k) $ is biased. Good R packages (**`{Amelia}`**, `{mi}`, `{mice}`, `{brms}`).
-
---
-
-.e[Disadvantages:] Results depend on quality of $\widehat{f(x|w,y)}$; May require more validation data, computationally expensive, statistically inefficient and doesn't seem to benefit much from larger datasets.
-
----
-
-### .border[Regression calibration directly adjusts for attenuation bias.]
-
-1. Use validation data to estimate the errors $\hat{\xi}$.
-
---
-
-2. Use $\hat{\xi}$ to correct the OLS estimate.
-
---
-
-3. Correct the standard errors using MLE or bootstrapping. 
-
---
-
-.e[Advantages:] Simple, fast.
-
---
-
-.e[Disadvantages:] Limited to OLS models. Requires an unbiased predictor $g(k)$. R support (`{mecor}` R package) is pretty new. 
-
----
-layout:true
-### .border[2SLS+GMM is designed for this specific problem]
-
-.left-column[![](images/Fong_Taylor.png)]
-
-*Regression calibration with a trick.*
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-]
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-2. Estimate $y = B^{2sls}\hat{x} + \varepsilon^{2sls}$. (Second-stage LS / regression calibration).
-
-]
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-2. Estimate $y = B^{2sls}\hat{x} + \varepsilon^{2sls}$.  (Second-stage LS / regression calibration).
-
-3. Estimate $y = B^{val}x^* + \varepsilon^{val}$. (Validation dataset model).
-
-]
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-2. Estimate $y = B^{2sls}\hat{x} + \varepsilon^{2sls}$.  (Second-stage LS / regression calibration).
-
-3. Estimate $y = B^{val}x^* + \varepsilon^{val}$. (Validation dataset model).
-
-4. Combine $B^{val}$ and $B^{2sls}$ using the generalized method of moments (GMM). 
-
-]
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-2. Estimate $y = B^{2sls}\hat{x} + \varepsilon^{2sls}$.  (Second-stage LS / regression calibration).
-
-3. Estimate $y = B^{val}x^* + \varepsilon^{val}$. (Validation dataset model).
-
-4. Combine $B^{val}$ and $B^{2sls}$ using the generalized method of moments (GMM). 
-
-Advantages: Accurate. Sometimes robust if biased predictor $g(k)$ is biased.  In theory, flexible to any models that can be fit using GMM. 
-
-]
-
-
----
-.right-column[
-
-1. Estimate $x = w + \xi$ to obtain $\hat{x}$. (First-stage LS).
-
-2. Estimate $y = B^{2sls}\hat{x} + \varepsilon^{2sls}$.  (Second-stage LS / regression calibration).
-
-3. Estimate $y = B^{val}x^* + \varepsilon^{val}$. (Validation dataset model).
-
-4. Combine $B^{val}$ and $B^{2sls}$ using the generalized method of moments (GMM). 
-
-Advantages: Accurate. Sometimes robust if biased predictor $g(k)$ is biased.  In theory, flexible to any models that can be fit using GMM. 
-
-Disadvantages: Implementation (`{predictionError}`) is new. API is cumbersome and only supports linear models. Not robust if $E(w\varepsilon) \ne 0$. GMM may be unfamiliar to audiences. 
-
-]
-
----
-layout:false
-### .border[Testing attention bias correction]
-
-<div class="my-header"></div>
-
-I've run simulations to test these approaches in several scenarios. 
-
-I simulate random data, fit 100 models and plot the average estimate and its variance.
-
-The model is not very good: about 70% accurate.
-
-Most plausible scenario: 
-
-y is continuous and normal-ish.
-
---
-
-$x$ is binary (human labels) $P(x)=0.5$.
-
---
-
-$w$ is the *continuous predictor* (e.g., probability) output of $f(x)$ (not binary predictions).
-
---
-
-if $w$ is binary, most methods struggle, but regression calibration and 2SLS+GMM can do okay.
-
----
-layout:false
-
-### .border[Example 1: estimator of the effect of x]
-
-.right-column[
-```{r echo=FALSE, message=FALSE, warning=FALSE, result='asis', dev='svg', fig.width=7.5, fig.asp=.625,cache=F}
-
-#plot.df <- 
-plot.df <- plot.df.example.1[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Feasible"),ordered=T),
-                                     N=factor(N),
-                                     m=factor(m))]
-
-plot.df <- plot.df[(variable=='x') & (m != 1000) & (m!=500) & (N!=10000) & !is.na(p.true.in.ci) & (method!="Multiple imputation (Classifier features unobserved)")]
-p <- ggplot(plot.df, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
-p <- p + geom_hline(aes(yintercept=0.2),linetype=2)
-
-p <- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4))
-
-print(p)
-
-# get gtable object
-
-```
-]
-.left-column[
-
-All methods work in this scenario
-
-Multiple imputation is inefficient. 
-
-]
-
-
----
-### .border[What about bias?]
-
-.left-column[
-.large[![](images/example_2_dag.png)]
-]
-
-.right-column[
-A few notes on this scenario. 
-
-$B_x = 0.2$, $B_g=-0.2$ and $sd(\varepsilon)=3$. So the signal-to-noise ratio is high. 
-
-$r$ can be concieved of as a missing feature in the predictive model $g(k)$ that is also correlated with $y$.
-
-For example $r$ might be the *race* of a commentor,  $x$ could be *racial harassment*, $y$ whether the commentor gets banned and $k$ only has textual features but human coders can see user profiles to know $r$. 
-
-]
-
----
-layout:false
-### .border[Example 2: Estimates of the effect of x ]
-
-.center[
-```{r echo=FALSE, message=FALSE, warning=FALSE, result='asis', dev='svg', fig.width=8, fig.asp=.625,cache=F}
-
-#plot.df <- 
-plot.df <- plot.df.example.2B[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Feasible"),ordered=T),
-                                     N=factor(N),
-                                     m=factor(m))]
-
-plot.df <- plot.df[(variable=='x') & (m != 1000) & (m!=500) & (N!=10000) & !is.na(p.true.in.ci) & (method!="Multiple imputation (Classifier features unobserved)")]
-p <- ggplot(plot.df, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
-p <- p + geom_hline(aes(yintercept=0.2),linetype=2)
-
-p <- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4))
-
-print(p)
-
-# get gtable object
-
-```
-]
----
-layout:false
-
-### .border[Example 2: Estimates of the effect of r]
-
-.center[
-```{r echo=FALSE, message=FALSE, warning=FALSE, result='asis', dev='svg', fig.width=8, fig.asp=.625,cache=F}
-
-#plot.df <- 
-plot.df <- plot.df.example.2B[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Feasible"),ordered=T),
-                                     N=factor(N),
-                                     m=factor(m))]
-
-plot.df <- plot.df[(variable=='g') & (m != 1000) & (m!=500) & (N!=10000) & !is.na(p.true.in.ci) & (method!="Multiple imputation (Classifier features unobserved)")]
-p <- ggplot(plot.df, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
-p <- p + geom_hline(aes(yintercept=-0.2),linetype=2)
-
-p <- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4))
-
-
-print(p)
-```
-]
----
-
-layout:false
-class:large
-
-###.border[Takeaways from example 2]
-
-Bias in the predictive model creates bias in hypothesis tests.
-
---
-
-Bias can be corrected *in this case*. 
-
---
-
-The next scenario has bias that's more tricky. 
-
---
-
-Multiple imputation helps, but doesn't fully correct the bias. 
-
----
-
-layout:false
-
-### .border[When will GMM+2SLS fail?]
-
-.large[.left-column[![](images/example_3_dag.png)]]
-
-.right-column[The catch with GMM:
-
-.emph[Exclusion restriction:] $E[w \varepsilon] = 0$.
-
-The restriction is violated if a variable $U$ causes both $K$ and $Y$ and $X$ causes $K$ (not visa-versa).
-
-]
-
-???
-
-GMM optimizes a model to a system of equations of which the exclusion restriction is one.  So if that assumption isn't true it will biased.
-
-This is a different assumption than that of OLS or GLM models.
-
----
-
-layout:false
-
-### .border[Example 3: Estimates of the effect of x]
-
-.center[
-```{r echo=FALSE, message=FALSE, warning=FALSE, result='asis', dev='svg', fig.width=8, fig.asp=.625,cache=F}
-
-#plot.df <- 
-plot.df <- plot.df.example.3[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Feasible"),ordered=T),
-                                     N=factor(N),
-                                     m=factor(m))]
-
-plot.df <- plot.df[(variable=='x') & (m != 1000) & (m!=500) & (N!=10000) & (method!="Multiple imputation (Classifier features unobserved)")]
-p <- ggplot(plot.df, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
-p <- p + geom_hline(aes(yintercept=0.2),linetype=2)
-
-p <- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4))
-
-
-print(p)
-```
-]
-
-
-
----
-
-### .border[Takaways]
-
-- Attenuation bias can be a big problem with noisy predictors—leading to small and biased estimates. 
-
-- For more general hypothesis tests or if the predictor is biased, measurement error can lead to false discovery. 
-
-- It's fixable with validation data—you may not need that much and you should already be getting it. 
-
-- This means it can be okay poor predictors for hypothesis testing.
-
-- The ecosystem is underdeveloped, but a lot of methods have been researched.
-
-- Take advantage of machine learning + big data and get precise estimates when the signal-to-noise ratio is high!
-
----
-layout:false
-
-### .border[Future work: Noise in the *outcome*]
-
-I've been focusing on noise in *covariates.* What if the predictive algorithm is used to measure the *outcome* $y$?
-
---
-
-This isn't a problem in the simplest case (linear regression with homoskedastic errors).  Noise in $y$ is projected into the error term.
-
---
-
-Noise in the outcome is still a problem if errors are heteroskedastic and for GLMs / non-linear regression (e.g., logistic regression).
-
---
-
-Multiple imputation (in theory) could help here. The other method's aren't designed for this case.
-
---
-
-Solving this problem could be an important methodological contribution with a very broad impact. 
-
----
-# .border[Questions?]
-
-Links to slides:[html](https://teblunthuis.cc/~nathante/slides/ecological_adaptation_ica_2022.html) [pdf](https://teblunthuis.cc/~nathante/slides/ecological_adaptation_ica_2022.pdf)
-
-Link to a messy git repository:[https://code.communitydata.science/ml_measurement_error_public.git](https://code.communitydata.science/ml_measurement_error_public.git)
-
-`r icons::fontawesome("envelope")` nathan.teblunthuis@northwestern.edu
-
-`r icons::fontawesome("twitter")` @groceryheist
-
-`r icons::fontawesome("globe")` [https://communitydata.science](https://communitydata.science)
-
-
-
-<!-- ### .border[Multiple imputation struggles with discrete variables] -->
-
-<!-- In my experiments I've found that the 2SLS+GMM method works well with a broader range of data types.  -->
-
-<!-- To illustrate, Example 3 is the same as Example 2, but with $x$ and $w$ as discrete variables.  -->
-
-<!-- Practicallly speaking, a continuous "score" $w$ is often available, and my opinion is that usually this is better + more informative than model predictions in all cases.  Continuous validation data may be more difficult to obtain, but it is often possible using techniques like pairwise comparison. -->
-<!-- layout:false -->
-<!-- ### .border[Example 3: Estimates of the effect of x ] -->
-
-<!-- .center[ -->
-<!-- ```{r echo=FALSE, message=FALSE, warning=FALSE, result='asis', dev='svg', fig.width=8, fig.asp=.625,cache=F} -->
-
-<!-- #plot.df <-  -->
-<!-- plot.df <- plot.df.example.2[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Feasible"),ordered=T), -->
-<!--                                      N=factor(N), -->
-<!--                                      m=factor(m))] -->
-
-<!-- plot.df <- plot.df[(variable=='x') & (m != 1000) & (m!=500) & (N!=5000) & (N!=10000) & !is.na(p.true.in.ci) & (method!="Multiple imputation (Classifier features unobserved)")] -->
-<!-- p <- ggplot(plot.df, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method)) -->
-<!-- p <- p + geom_hline(aes(yintercept=0.2),linetype=2) -->
-
-<!-- p <- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4)) -->
-
-<!-- print(p) -->
-
-<!-- # get gtable object -->
-
-<!-- .large[.left [![](images/example_2_dag.png)]] -->
-
-<!-- There are at two general ways using a predictive model can introduce bias: *attenuation*, and *confounding.* -->
-
-<!-- Counfounding can be broken down into 4 types: -->
-
-<!-- .right[Confounding on $X$ by observed variables -->
-	
-<!-- 	Confounding on $Y$ by observed variables -->
-<!-- ] -->
-
-<!-- .left[Confounding on $X$ by *un*observed variables -->
-	
-<!-- 	Confounding on $Y$ by *un*observed variables -->
-<!-- ] -->
-
-<!-- Attenuation and the top-right column can be dealt with relative ease using a few different methods. -->
-
-<!-- The bottom-left column can be addressed, but so far I haven't found a magic bullet. -->
-
-<!-- The left column is pretty much a hopeless situation. -->

presentations/ica_hackathon_2022/ica_hackathon_2022.html

@@ -1,757 +0,0 @@
-<!DOCTYPE html>
-<html lang="" xml:lang="">
-  <head>
-    <title>How good of a model do you need? Accounting for classification errors in machine assisted content analysis.</title>
-    <meta charset="utf-8" />
-    <meta name="author" content="Nathan TeBlunthuis" />
-    <script src="libs/header-attrs-2.14/header-attrs.js"></script>
-    <link href="libs/remark-css-0.0.1/default.css" rel="stylesheet" />
-    <link rel="stylesheet" href="my-theme.css" type="text/css" />
-    <link rel="stylesheet" href="fontawesome.min.css" type="text/css" />
-  </head>
-  <body>
-    <textarea id="source">
-
-
-class: center, middle, narrow
-
-&lt;script type='javascript'&gt;
-window.MathJax = {
-  loader: {load: ['[tex]/xcolor']},
-  tex: {packages: {'[+]': ['xcolor']}}
-};
-&lt;/script&gt;
-
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-
-###  .title-heading[Unlocking the power of big data: The importance of measurement error in machine assisted content analysis]
-## Nathan TeBlunthuis
-
-&lt;img src="images/nu_logo.png" height="170px" style="padding:21px"/&gt; &lt;img src="images/uw_logo.png" height="170px" style="padding:21px"/&gt; &lt;img src="images/cdsc_logo.png" height="170px" style="padding:21px"/&gt;
-
-
-nathan.teblunthuis@northwestern.edu
-
-[https://teblunthuis.cc](https://teblunthuis.cc)
-
-???
-
-This talk will be me presenting my "lab notebook" and not a polished research talk.  Maybe it would be a good week of a graduate seminar? In sum, machine assisted content analysis has unique limitations and threats to validity that I wanted to understand better.  I've learned how the noise introduced by predictive models can result in misleading statistical inferences, but that a sample of human-labeled validation data can often be used to account for this noise and obtain accurate inferences in the end.  Statistical knowledge of this problem and computational tools for addressing are still in development.  My goals for this presentation are to start sharing this information with the community and hopeful to stimulate us to work on extending existing approaches or using them in our work.
-
-This is going to be a boring talk about some *very* technical material. If you're not that interested please return to your hackathon. Please interrupt me if I'm going too fast for you or if you don't understand something.  I will try to move quickly in the interests of those wishing to wrap up their hackathon projects. I will also ask you to show hands once or twice, if you are already familiar with some concepts that it might be expedient to skip.
-
----
-
-class:center, middle, inverse
-## Machine assistent content analysis (MACA)
-
-???
-
-I'm going to start by defining a study design that is increasingly common, especially in Communication and Political Science, but also across the social sciences and beyond. I call it *machine assisted content analysis* (MACA).
-
----
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Machine assisted content analysis (MACA) uses machine learning for scientific measurement.]
-
-.emph[Content analysis:] Statistical analysis of variables measured by human labeling ("coding") of content.  This might be simple categorical labels, or maybe more advanced annotations.
-
---
-
-*Downside:* Human labeling is *a lot* of work.
-
---
-
-.emph[Machine assisted content analysis:] Use a *predictive algorithm* (often trained on human-made labels) to measure variables for use in a downstream *primary analysis.*
-
---
-
-*Downside:*  Algorithms can be *biased* and *inaccurate* in ways that could invalidate the statistical analysis.
-
-
-???
-
-A machine assisted content analysis can be part of a more complex or more powerful study design (e.g., an experiment, time series analysis &amp;c). 
-
----
-
-
-&lt;!-- &lt;div class="my-header"&gt;&lt;/div&gt; --&gt;
-
-&lt;!-- ### .border[Hypothetical Example: Predicting Racial Harassement in Social Media Comments] --&gt;
-
----
-class:large 
-
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[How can MACA go wrong?]
-
-Algorithms can be *biased* and *error prone* (*noisy*).
-
---
-
-Predictor bias is a potentially difficult problem that requires causal inference methods. I'll focus on *noise* for now.
-
---
-
-Noise in the predictive model introduces bias in the primary analysis.
-
---
-
-.indent[We can reduce and sometimes even *eliminate* this bias introduced by noise.]
-
----
-layout:true
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Example 1: An unbiased, but noisy classifier]
-
-.large[.left-column[![](images/example_1_dag.png)]]
-
-???
-
-Please show hands if you are familiar with causal graphs or baysian networks.  Should I explain what this diagram means?
-
-
----
-
-.right-column[
-`\(x\)` is *partly observed* because we have *validation data* `\(x^*\)`.
-]
-
----
-
-
-.right-column[
-`\(x\)` is *partly observed* because we have *validation data* `\(x^*\)`.
-
-`\(k\)` are the *features* used by the *predictive model* `\(g(k)\)`.
-
-]
-
----
-
-.right-column[
-`\(x\)` is *partly observed* because we have *validation data* `\(x^*\)`.
-
-`\(k\)` are the *features* used by the *predictive model* `\(g(k)\)`.
-
-The predictions `\(w\)` are a *proxy variable*  `\(g(k) = \hat{x} = w\)`.
-
-]
-
----
-
-
-.right-column[
-`\(x\)` is *partly observed* because we have *validation data* `\(x^*\)`.
-
-`\(k\)` are the *features* used by the *predictive model* `\(g(k)\)`.
-
-The predictions `\(w\)` are a *proxy variable*  `\(g(k) = \hat{x} = w\)`.
-
-`\(x = w + \xi\)` because the predictive model makes errors.
-
-]
-
----
-
-
-layout:true
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Noise in a *covariate* creates *attenuation bias*.]
-
-.large[.left-column[![](images/example_1_dag.png)]]
-
----
-.right-column[
-
-We want to estimate, `\(y = Bx + \varepsilon\)`, but we estimate `\(y = Bw + \varepsilon\)` instead.
-
-`\(x = w + \xi\)` because the predictive model makes errors.
- 
-]
----
-
-.right-column[
-
-We want to estimate, `\(y = Bx + \varepsilon\)`, but we estimate `\(y = Bw + \varepsilon\)` instead.
-
-`\(x = w + \xi\)` because the predictive model makes errors.
-
- 
-Assume `\(g(k)\)` is *unbiased* so `\(E(\xi)=0\)`. Also assume error is *nondifferential* so `\(E(\xi y)=0\)`:
-
-]
-
----
-
-.right-column[
-
-We want to estimate, `\(y = Bx + \varepsilon\)`, but we estimate `\(y = Bw + \varepsilon\)` instead.
-
-`\(x = w + \xi\)` because the predictive model makes errors.
-
-Assume `\(g(k)\)` is *unbiased* so `\(E(\xi)=0\)`. Also assume error is *nondifferential* so `\(E(\xi y)=0\)`:
-
-`$$\widehat{B_w}^{ols}=\frac{\sum^n_{j=j}{(x_j + \xi_j - \overline{(x + \xi)})}(y_j - \bar{y})}{\sum_{j=1}^n{(x_j + \xi_j - \overline{(x+\xi)})^2}} = \frac{\sum^n_{j=j}{(x_j - \bar{x})(y_j -
- \bar{y})}}{\sum_{j=1}^n{(x_j + \xi_j - \bar{x}){^2}}}$$`
-
-]
-
----
-
-.right-column[
-
-We want to estimate, `\(y = Bx + \varepsilon\)`, but we estimate `\(y = Bw + \varepsilon\)` instead.
-
-`\(x = w + \xi\)` because the predictive model makes errors.
-
-Assume `\(g(k)\)` is *unbiased* so `\(E(\xi)=0\)`. Also assume error is *nondifferential* so `\(E(\xi y)=0\)`:
-
-`$$\widehat{B_w}^{ols}=\frac{\sum^n_{j=j}{(x_j + \xi_j - \overline{(x + \xi)})}(y_j - \bar{y})}{\sum_{j=1}^n{(x_j + \xi_j - \overline{(x+\xi)})^2}} = \frac{\sum^n_{j=j}{(x_j - \bar{x})(y_j -
- \bar{y})}}{\sum_{j=1}^n{(x_j + \color{red}{\xi_j} - \bar{x})\color{red}{^2}}}$$`
-
-In this scenario, it's clear that `\(\widehat{B_w}^{ols} &lt; B_x\)`.
-
-
-]
-
-
-???
-
-Please raise your hands if you're familiar with attenuation bias.  I expect that its covered in some graduate stats classes, but not universally.
-
----
-class:large
-layout:false
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Beyond attenuation bias]
-.larger[Measurement error can theaten validity because:]
-
-- Attenuation bias *spreads* (e.g., to marginal effects as illustrated later).
-
---
-
-- Measurement error can be *differential*— not distributed evenly and possible correlated with `\(x\)`, `\(y\)`, or `\(\varepsilon\)`.
-
---
-
-- *Bias can be away from 0* in GLMs and nonlinear models or if measurement error is differential.
-
---
-
-- *Confounding* if the *predictive model is biased* introducing a correlation the measurement error and the residuals `\((E[\xi\varepsilon]=0)\)`. 
-
-
----
-
-class:large
-layout:false
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Correcting measurement error]
-
-There's a vast literature in statistics on measurement error. Mostly about noise you'd find in sensors. Lots of ideas. No magic bullets.
-
---
-
-I'm going to briefly cover 3 different approaches: *multiple imputation*,  *regression calibration* and *2SLS+GMM*.
-
---
-
-These all depend on *validation data*. I'm going to ignore where this comes from, but assume it's a random sample of the hypothesis testing dataset. 
-
---
-
-You can *and should* use it to improve your statistical estimates. 
-
----
-
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-### .border[Multiple Imputation (MI) treats Measurement Error as a Missing Data Problem]
-
-1. Use validation data to estimate `\(f(x|w,y)\)`, a probabilistic model of `\(x\)`.
-
---
-
-2. *Sample* `\(m\)` datasets from `\(\widehat{f(x|w,y)}\)`.
-
---
-
-3. Run your analysis on each of the `\(m\)` datasets.
-
---
-
-4. Average the results from the `\(m\)` analyses using Rubin's rules.
-
---
-
-.e[Advantages:] *Very flexible!* Sometimes can work if the predictor $g(k) $ is biased. Good R packages (**`{Amelia}`**, `{mi}`, `{mice}`, `{brms}`).
-
---
-
-.e[Disadvantages:] Results depend on quality of `\(\widehat{f(x|w,y)}\)`; May require more validation data, computationally expensive, statistically inefficient and doesn't seem to benefit much from larger datasets.
-
----
-
-### .border[Regression calibration directly adjusts for attenuation bias.]
-
-1. Use validation data to estimate the errors `\(\hat{\xi}\)`.
-
---
-
-2. Use `\(\hat{\xi}\)` to correct the OLS estimate.
-
---
-
-3. Correct the standard errors using MLE or bootstrapping. 
-
---
-
-.e[Advantages:] Simple, fast.
-
---
-
-.e[Disadvantages:] Limited to OLS models. Requires an unbiased predictor `\(g(k)\)`. R support (`{mecor}` R package) is pretty new. 
-
----
-layout:true
-### .border[2SLS+GMM is designed for this specific problem]
-
-.left-column[![](images/Fong_Taylor.png)]
-
-*Regression calibration with a trick.*
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-]
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-2. Estimate `\(y = B^{2sls}\hat{x} + \varepsilon^{2sls}\)`. (Second-stage LS / regression calibration).
-
-]
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-2. Estimate `\(y = B^{2sls}\hat{x} + \varepsilon^{2sls}\)`.  (Second-stage LS / regression calibration).
-
-3. Estimate `\(y = B^{val}x^* + \varepsilon^{val}\)`. (Validation dataset model).
-
-]
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-2. Estimate `\(y = B^{2sls}\hat{x} + \varepsilon^{2sls}\)`.  (Second-stage LS / regression calibration).
-
-3. Estimate `\(y = B^{val}x^* + \varepsilon^{val}\)`. (Validation dataset model).
-
-4. Combine `\(B^{val}\)` and `\(B^{2sls}\)` using the generalized method of moments (GMM). 
-
-]
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-2. Estimate `\(y = B^{2sls}\hat{x} + \varepsilon^{2sls}\)`.  (Second-stage LS / regression calibration).
-
-3. Estimate `\(y = B^{val}x^* + \varepsilon^{val}\)`. (Validation dataset model).
-
-4. Combine `\(B^{val}\)` and `\(B^{2sls}\)` using the generalized method of moments (GMM). 
-
-Advantages: Accurate. Sometimes robust if biased predictor `\(g(k)\)` is biased.  In theory, flexible to any models that can be fit using GMM. 
-
-]
-
-
----
-.right-column[
-
-1. Estimate `\(x = w + \xi\)` to obtain `\(\hat{x}\)`. (First-stage LS).
-
-2. Estimate `\(y = B^{2sls}\hat{x} + \varepsilon^{2sls}\)`.  (Second-stage LS / regression calibration).
-
-3. Estimate `\(y = B^{val}x^* + \varepsilon^{val}\)`. (Validation dataset model).
-
-4. Combine `\(B^{val}\)` and `\(B^{2sls}\)` using the generalized method of moments (GMM). 
-
-Advantages: Accurate. Sometimes robust if biased predictor `\(g(k)\)` is biased.  In theory, flexible to any models that can be fit using GMM. 
-
-Disadvantages: Implementation (`{predictionError}`) is new. API is cumbersome and only supports linear models. Not robust if `\(E(w\varepsilon) \ne 0\)`. GMM may be unfamiliar to audiences. 
-
-]
-
----
-layout:false
-### .border[Testing attention bias correction]
-
-&lt;div class="my-header"&gt;&lt;/div&gt;
-
-I've run simulations to test these approaches in several scenarios. 
-
-The model is not very good: about 70% accurate.
-
-Most plausible scenario: 
-
-y is continuous and normal-ish.
-
---
-
-`\(x\)` is binary (human labels) `\(P(x)=0.5\)`.
-
---
-
-`\(w\)` is the *continuous predictor* (e.g., probability) output of `\(f(x)\)` (not binary predictions).
-
---
-
-if `\(w\)` is binary, most methods struggle, but regression calibration and 2SLS+GMM can do okay.
-
----
-layout:false
-
-### .border[Example 1: estimator of the effect of x]
-
-.right-column[
-![](ica_hackathon_2022_files/figure-html/unnamed-chunk-2-1.svg)&lt;!-- --&gt;
-]
-.left-column[
-
-All methods work in this scenario
-
-Multiple imputation is inefficient. 
-
-]
-
-
----
-### .border[What about bias?]
-
-.left-column[
-.large[![](images/example_2_dag.png)]
-]
-
-.right-column[
-A few notes on this scenario. 
-
-`\(B_x = 0.2\)`, `\(B_g=-0.2\)` and `\(sd(\varepsilon)=3\)`. So the signal-to-noise ratio is high. 
-
-`\(r\)` can be concieved of as a missing feature in the predictive model `\(g(k)\)` that is also correlated with `\(y\)`.
-
-For example `\(r\)` might be the *race* of a commentor,  `\(x\)` could be *racial harassment*, `\(y\)` whether the commentor gets banned and `\(k\)` only has textual features but human coders can see user profiles to know `\(r\)`. 
-
-]
-
----
-layout:false
-### .border[Example 2: Estimates of the effect of x ]
-
-.center[
-![](ica_hackathon_2022_files/figure-html/unnamed-chunk-3-1.svg)&lt;!-- --&gt;
-]
----
-layout:false
-
-### .border[Example 2: Estimates of the effect of r]
-
-.center[
-![](ica_hackathon_2022_files/figure-html/unnamed-chunk-4-1.svg)&lt;!-- --&gt;
-]
----
-
-layout:false
-class:large
-
-###.border[Takeaways from example 2]
-
-Bias in the predictive model creates bias in hypothesis tests.
-
---
-
-Bias can be corrected *in this case*. 
-
---
-
-The next scenario has bias that's more tricky. 
-
---
-
-Multiple imputation helps, but doesn't fully correct the bias. 
-
----
-
-layout:false
-
-### .border[When will GMM+2SLS fail?]
-
-.large[.left-column[![](images/example_3_dag.png)]]
-
-.right-column[The catch with GMM:
-
-.emph[Exclusion restriction:] `\(E[w \varepsilon] = 0\)`.
-
-The restriction is violated if a variable `\(U\)` causes both `\(K\)` and `\(Y\)` and `\(X\)` causes `\(K\)` (not visa-versa).
-
-]
-
-???
-
-GMM optimizes a model to a system of equations of which the exclusion restriction is one.  So if that assumption isn't true it will biased.
-
-This is a different assumption than that of OLS or GLM models.
-
----
-
-layout:false
-
-### .border[Example 3: Estimates of the effect of x]
-
-.center[
-![](ica_hackathon_2022_files/figure-html/unnamed-chunk-5-1.svg)&lt;!-- --&gt;
-]
-
-
-
----
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-### .border[Takaways]
-
-- Attenuation bias can be a big problem with noisy predictors—leading to small and biased estimates. 
-
-- For more general hypothesis tests or if the predictor is biased, measurement error can lead to false discovery. 
-
-- It's fixable with validation data—you may not need that much and you should already be getting it. 
-
-- This means it can be okay poor predictors for hypothesis testing.
-
-- The ecosystem is underdeveloped, but a lot of methods have been researched.
-
-- Take advantage of machine learning + big data and get precise estimates when the signal-to-noise ratio is high!
-
----
-layout:false
-
-### .border[Future work: Noise in the *outcome*]
-
-I've been focusing on noise in *covariates.* What if the predictive algorithm is used to measure the *outcome* `\(y\)`?
-
---
-
-This isn't a problem in the simplest case (linear regression with homoskedastic errors).  Noise in `\(y\)` is projected into the error term.
-
---
-
-Noise in the outcome is still a problem if errors are heteroskedastic and for GLMs / non-linear regression (e.g., logistic regression).
-
---
-
-Multiple imputation (in theory) could help here. The other method's aren't designed for this case.
-
---
-
-Solving this problem could be an important methodological contribution with a very broad impact. 
-
----
-# .border[Questions?]
-
-Links to slides:[html](https://teblunthuis.cc/~nathante/slides/ecological_adaptation_ica_2022.html) [pdf](https://teblunthuis.cc/~nathante/slides/ecological_adaptation_ica_2022.pdf)
-
-Link to a messy git repository: 
-
-&lt;i class="fa fa-envelope" aria-hidden='true'&gt;&lt;/i&gt; nathan.teblunthuis@northwestern.edu
-
-&lt;i class="fa fa-twitter" aria-hidden='true'&gt;&lt;/i&gt; @groceryheist
-
-&lt;i class="fa fa-globe" aria-hidden='true'&gt;&lt;/i&gt; [https://communitydata.science](https://communitydata.science)
-
-
-
-&lt;!-- ### .border[Multiple imputation struggles with discrete variables] --&gt;
-
-&lt;!-- In my experiments I've found that the 2SLS+GMM method works well with a broader range of data types.  --&gt;
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-&lt;!-- To illustrate, Example 3 is the same as Example 2, but with `\(x\)` and `\(w\)` as discrete variables.  --&gt;
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-&lt;!-- Practicallly speaking, a continuous "score" `\(w\)` is often available, and my opinion is that usually this is better + more informative than model predictions in all cases.  Continuous validation data may be more difficult to obtain, but it is often possible using techniques like pairwise comparison. --&gt;
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-&lt;!-- p &lt;- p + geom_hline(aes(yintercept=0.2),linetype=2) --&gt;
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-&lt;!-- p &lt;- p + geom_pointrange() + facet_grid(m~N,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4)) --&gt;
-
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-
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-
-&lt;!-- .large[.left [![](images/example_2_dag.png)]] --&gt;
-
-&lt;!-- There are at two general ways using a predictive model can introduce bias: *attenuation*, and *confounding.* --&gt;
-
-&lt;!-- Counfounding can be broken down into 4 types: --&gt;
-
-&lt;!-- .right[Confounding on `\(X\)` by observed variables --&gt;
-	
-&lt;!-- 	Confounding on `\(Y\)` by observed variables --&gt;
-&lt;!-- ] --&gt;
-
-&lt;!-- .left[Confounding on `\(X\)` by *un*observed variables --&gt;
-	
-&lt;!-- 	Confounding on `\(Y\)` by *un*observed variables --&gt;
-&lt;!-- ] --&gt;
-
-&lt;!-- Attenuation and the top-right column can be dealt with relative ease using a few different methods. --&gt;
-
-&lt;!-- The bottom-left column can be addressed, but so far I haven't found a magic bullet. --&gt;
-
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-   Feel free (nay, compelled) to edit, append, and
-   manipulate this file as you see fit. */
-
-
-@media print {
-
-	/* SECTION 1: Set default width, margin, float, and
-	   background. This prevents elements from extending
-	   beyond the edge of the printed page, and prevents
-	   unnecessary background images from printing */
-	html {
-		background: #fff;
-		width: auto;
-		height: auto;
-		overflow: visible;
-	}
-	body {
-		background: #fff;
-		font-size: 20pt;
-		width: auto;
-		height: auto;
-		border: 0;
-		margin: 0 5%;
-		padding: 0;
-		overflow: visible;
-		float: none !important;
-	}
-
-	/* SECTION 2: Remove any elements not needed in print.
-	   This would include navigation, ads, sidebars, etc. */
-	.nestedarrow,
-	.controls,
-	.fork-reveal,
-	.share-reveal,
-	.state-background,
-	.reveal .progress,
-	.reveal .backgrounds {
-		display: none !important;
-	}
-
-	/* SECTION 3: Set body font face, size, and color.
-	   Consider using a serif font for readability. */
-	body, p, td, li, div {
-		font-size: 20pt!important;
-		font-family: Georgia, "Times New Roman", Times, serif !important;
-		color: #000;
-	}
-
-	/* SECTION 4: Set heading font face, sizes, and color.
-	   Differentiate your headings from your body text.
-	   Perhaps use a large sans-serif for distinction. */
-	h1,h2,h3,h4,h5,h6 {
-		color: #000!important;
-		height: auto;
-		line-height: normal;
-		font-family: Georgia, "Times New Roman", Times, serif !important;
-		text-shadow: 0 0 0 #000 !important;
-		text-align: left;
-		letter-spacing: normal;
-	}
-	/* Need to reduce the size of the fonts for printing */
-	h1 { font-size: 28pt !important;  }
-	h2 { font-size: 24pt !important; }
-	h3 { font-size: 22pt !important; }
-	h4 { font-size: 22pt !important; font-variant: small-caps; }
-	h5 { font-size: 21pt !important; }
-	h6 { font-size: 20pt !important; font-style: italic; }
-
-	/* SECTION 5: Make hyperlinks more usable.
-	   Ensure links are underlined, and consider appending
-	   the URL to the end of the link for usability. */
-	a:link,
-	a:visited {
-		color: #000 !important;
-		font-weight: bold;
-		text-decoration: underline;
-	}
-	/*
-	.reveal a:link:after,
-	.reveal a:visited:after {
-		content: " (" attr(href) ") ";
-		color: #222 !important;
-		font-size: 90%;
-	}
-	*/
-
-
-	/* SECTION 6: more reveal.js specific additions by @skypanther */
-	ul, ol, div, p {
-		visibility: visible;
-		position: static;
-		width: auto;
-		height: auto;
-		display: block;
-		overflow: visible;
-		margin: 0;
-		text-align: left !important;
-	}
-	.reveal pre,
-	.reveal table {
-		margin-left: 0;
-		margin-right: 0;
-	}
-	.reveal pre code {
-		padding: 20px;
-		border: 1px solid #ddd;
-	}
-	.reveal blockquote {
-		margin: 20px 0;
-	}
-	.reveal .slides {
-		position: static !important;
-		width: auto !important;
-		height: auto !important;
-
-		left: 0 !important;
-		top: 0 !important;
-		margin-left: 0 !important;
-		margin-top: 0 !important;
-		padding: 0 !important;
-		zoom: 1 !important;
-
-		overflow: visible !important;
-		display: block !important;
-
-		text-align: left !important;
-		-webkit-perspective: none;
-		   -moz-perspective: none;
-		    -ms-perspective: none;
-		        perspective: none;
-
-		-webkit-perspective-origin: 50% 50%;
-		   -moz-perspective-origin: 50% 50%;
-		    -ms-perspective-origin: 50% 50%;
-		        perspective-origin: 50% 50%;
-	}
-	.reveal .slides section {
-		visibility: visible !important;
-		position: static !important;
-		width: auto !important;
-		height: auto !important;
-		display: block !important;
-		overflow: visible !important;
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-		left: 0 !important;
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-		margin-top: 0 !important;
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-		   -moz-transform-style: flat !important;
-		    -ms-transform-style: flat !important;
-		        transform-style: flat !important;
-
-		-webkit-transform: none !important;
-		   -moz-transform: none !important;
-		    -ms-transform: none !important;
-		        transform: none !important;
-
-		-webkit-transition: none !important;
-		   -moz-transition: none !important;
-		    -ms-transition: none !important;
-		        transition: none !important;
-	}
-	.reveal .slides section.stack {
-		padding: 0 !important;
-	}
-	.reveal section:last-of-type {
-		page-break-after: avoid !important;
-	}
-	.reveal section .fragment {
-		opacity: 1 !important;
-		visibility: visible !important;
-
-		-webkit-transform: none !important;
-		   -moz-transform: none !important;
-		    -ms-transform: none !important;
-		        transform: none !important;
-	}
-	.reveal section img {
-		display: block;
-		margin: 15px 0px;
-		background: rgba(255,255,255,1);
-		border: 1px solid #666;
-		box-shadow: none;
-	}
-
-	.reveal section small {
-		font-size: 0.8em;
-	}
-
-}  
-</script>
-
-
-<script id="pdf-css" type="application/dynamic-css">
-    
-/**
- * This stylesheet is used to print reveal.js
- * presentations to PDF.
- *
- * https://github.com/hakimel/reveal.js#pdf-export
- */
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-* {
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-}
-
-body {
-	margin: 0 auto !important;
-	border: 0;
-	padding: 0;
-	float: none !important;
-	overflow: visible;
-}
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-html {
-	width: 100%;
-	height: 100%;
-	overflow: visible;
-}
-
-/* Remove any elements not needed in print. */
-.nestedarrow,
-.reveal .controls,
-.reveal .progress,
-.reveal .playback,
-.reveal.overview,
-.fork-reveal,
-.share-reveal,
-.state-background {
-	display: none !important;
-}
-
-h1, h2, h3, h4, h5, h6 {
-	text-shadow: 0 0 0 #000 !important;
-}
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-.reveal pre code {
-	overflow: hidden !important;
-	font-family: Courier, 'Courier New', monospace !important;
-}
-
-ul, ol, div, p {
-	visibility: visible;
-	position: static;
-	width: auto;
-	height: auto;
-	display: block;
-	overflow: visible;
-	margin: auto;
-}
-.reveal {
-	width: auto !important;
-	height: auto !important;
-	overflow: hidden !important;
-}
-.reveal .slides {
-	position: static;
-	width: 100%;
-	height: auto;
-
-	left: auto;
-	top: auto;
-	margin: 0 !important;
-	padding: 0 !important;
-
-	overflow: visible;
-	display: block;
-
-	-webkit-perspective: none;
-	   -moz-perspective: none;
-	    -ms-perspective: none;
-	        perspective: none;
-
-	-webkit-perspective-origin: 50% 50%; /* there isn't a none/auto value but 50-50 is the default */
-	   -moz-perspective-origin: 50% 50%;
-	    -ms-perspective-origin: 50% 50%;
-	        perspective-origin: 50% 50%;
-}
-
-.reveal .slides section {
-	page-break-after: always !important;
-
-	visibility: visible !important;
-	position: relative !important;
-	display: block !important;
-	position: relative !important;
-
-	margin: 0 !important;
-	padding: 0 !important;
-	box-sizing: border-box !important;
-	min-height: 1px;
-
-	opacity: 1 !important;
-
-	-webkit-transform-style: flat !important;
-	   -moz-transform-style: flat !important;
-	    -ms-transform-style: flat !important;
-	        transform-style: flat !important;
-
-	-webkit-transform: none !important;
-	   -moz-transform: none !important;
-	    -ms-transform: none !important;
-	        transform: none !important;
-}
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-.reveal section.stack {
-	margin: 0 !important;
-	padding: 0 !important;
-	page-break-after: avoid !important;
-	height: auto !important;
-	min-height: auto !important;
-}
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-.reveal img {
-	box-shadow: none;
-}
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-.reveal .roll {
-	overflow: visible;
-	line-height: 1em;
-}
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-/* Slide backgrounds are placed inside of their slide when exporting to PDF */
-.reveal section .slide-background {
-	display: block !important;
-	position: absolute;
-	top: 0;
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-	z-index: -1;
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-/* All elements should be above the slide-background */
-.reveal section>* {
-	position: relative;
-	z-index: 1;
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-/* Display slide speaker notes when 'showNotes' is enabled */
-.reveal .speaker-notes-pdf {
-	display: block;
-	width: 100%;
-	max-height: none;
-	left: auto;
-	top: auto;
-	z-index: 100;
-}
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-/* Display slide numbers when 'slideNumber' is enabled */
-.reveal .slide-number-pdf {
-	display: block;
-	position: absolute;
-	font-size: 14px;
-}
-
-</script>
-
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-<script>
-var style = document.createElement( 'style' );
-style.type = 'text/css';
-var style_script_id = window.location.search.match( /print-pdf/gi ) ? 'pdf-css' : 'paper-css';
-var style_script = document.getElementById(style_script_id).text;
-style.innerHTML = style_script;
-document.getElementsByTagName('head')[0].appendChild(style);
-</script>
-
-$for(header-includes)$
-    $header-includes$
-$endfor$
-</head>
-<body>
-$for(include-before)$
-$include-before$
-$endfor$
-  <div class="reveal">
-    <div class="slides">
-
-
-
-<!--
-$if(title)$
-<section>
-    <h1 class="title">$title$</h1>
-$if(subtitle)$
-  <h1 class="subtitle">$subtitle$</h1>
-$endif$
-$for(author)$
-    <h2 class="author">$author$</h2>
-$endfor$
-$if(date)$
-    <h3 class="date">$date$</h3>
-$endif$
-</section>
-$endif$
-$if(toc)$
-<section id="$idprefix$TOC">
-$toc$
-</section>
-$endif$
--->
-
-$body$
-    </div>
-  </div>
-
-  <script src="$revealjs-url$/lib/js/head.min.js"></script>
-  <script src="$revealjs-url$/js/reveal.js"></script>
-
-  <script>
-
-      // Full list of configuration options available at:
-      // https://github.com/hakimel/reveal.js#configuration
-      Reveal.initialize({
-$if(controls)$
-        // Display controls in the bottom right corner
-        controls: $controls$,
-$endif$
-$if(progress)$
-        // Display a presentation progress bar
-        progress: $progress$,
-$endif$
-$if(slideNumber)$
-        // Display the page number of the current slide
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-$endif$
-$if(history)$
-        // Push each slide change to the browser history
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-$endif$
-$if(keyboard)$
-        // Enable keyboard shortcuts for navigation
-        keyboard: $keyboard$,
-$endif$
-$if(overview)$
-        // Enable the slide overview mode
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-$endif$
-$if(center)$
-        // Vertical centering of slides
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-$endif$
-$if(touch)$
-        // Enables touch navigation on devices with touch input
-        touch: $touch$,
-$endif$
-$if(loop)$
-        // Loop the presentation
-        loop: $loop$,
-$endif$
-$if(rtl)$
-        // Change the presentation direction to be RTL
-        rtl: $rtl$,
-$endif$
-$if(fragments)$
-        // Turns fragments on and off globally
-        fragments: $fragments$,
-$endif$
-$if(embedded)$
-        // Flags if the presentation is running in an embedded mode,
-        // i.e. contained within a limited portion of the screen
-        embedded: $embedded$,
-$endif$
-$if(help)$
-        // Flags if we should show a help overlay when the questionmark
-        // key is pressed
-        help: $help$,
-$endif$
-$if(autoSlide)$
-        // Number of milliseconds between automatically proceeding to the
-        // next slide, disabled when set to 0, this value can be overwritten
-        // by using a data-autoslide attribute on your slides
-        autoSlide: $autoSlide$,
-$endif$
-$if(autoSlideStoppable)$
-        // Stop auto-sliding after user input
-        autoSlideStoppable: $autoSlideStoppable$,
-$endif$
-$if(mouseWheel)$
-        // Enable slide navigation via mouse wheel
-        mouseWheel: $mouseWheel$,
-$endif$
-$if(hideAddressBar)$
-        // Hides the address bar on mobile devices
-        hideAddressBar: $hideAddressBar$,
-$endif$
-$if(previewLinks)$
-        // Opens links in an iframe preview overlay
-        previewLinks: $previewLinks$,
-$endif$
-$if(transition)$
-        // Transition style
-        transition: '$transition$', // none/fade/slide/convex/concave/zoom
-$endif$
-$if(transitionSpeed)$
-        // Transition speed
-        transitionSpeed: '$transitionSpeed$', // default/fast/slow
-$endif$
-$if(backgroundTransition)$
-        // Transition style for full page slide backgrounds
-        backgroundTransition: '$backgroundTransition$', // none/fade/slide/convex/concave/zoom
-$endif$
-$if(viewDistance)$
-        // Number of slides away from the current that are visible
-        viewDistance: $viewDistance$,
-$endif$
-$if(parallaxBackgroundImage)$
-        // Parallax background image
-        parallaxBackgroundImage: '$parallaxBackgroundImage$', // e.g. "'https://s3.amazonaws.com/hakim-static/reveal-js/reveal-parallax-1.jpg'"
-$endif$
-$if(parallaxBackgroundSize)$
-        // Parallax background size
-        parallaxBackgroundSize: '$parallaxBackgroundSize$', // CSS syntax, e.g. "2100px 900px"
-$endif$
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-        // Amount to move parallax background (horizontal and vertical) on slide change
-        // Number, e.g. 100
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-$endif$
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-        parallaxBackgroundVertical: '$parallaxBackgroundVertical$',
-$endif$
-$if(width)$
-        // The "normal" size of the presentation, aspect ratio will be preserved
-        // when the presentation is scaled to fit different resolutions. Can be
-        // specified using percentage units.
-        width: $width$,
-$endif$
-$if(height)$
-        height: $height$,
-$endif$
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-        // Factor of the display size that should remain empty around the content
-        margin: $margin$,
-$endif$
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-        // Bounds for smallest/largest possible scale to apply to content
-        minScale: $minScale$,
-$endif$
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-        maxScale: $maxScale$,
-$endif$
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-$if(plugin-menu)$
-        menu: {
-$if(menu-side)$
-          side: $menu-side$,
-$endif$   
-$if(menu-numbers)$
-          numbers: $menu-numbers$,
-$endif$    
-$if(menu-titleSelector)$
-          titleSelector: $menu-titleSelector$,
-$endif$    
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-          hideMissingTitles: $menu-hideMissingTitles$,
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-        chalkboard: {
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-          src: $chalkboard-src$,
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-          pen: $chalkboard-pen$,
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-        },
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-        keyboard: {
-          67: function() { RevealChalkboard.toggleNotesCanvas() },    // toggle notes canvas when 'c' is pressed
-          66: function() { RevealChalkboard.toggleChalkboard() }, // toggle chalkboard when 'b' is pressed
-          46: function() { RevealChalkboard.clear() },    // clear chalkboard when 'DEL' is pressed
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-        dependencies: [
-$if(plugin-notes)$
-          { src: '$revealjs-url$/plugin/notes/notes.js', async: true },
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-          { src: '$revealjs-url$/plugin/search/search.js', async: true },
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-$endif$
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-      Reveal.addEventListener( 'slidechanged', function(event) {  
-        window.jQuery(event.previousSlide).trigger('hidden');
-        window.jQuery(event.currentSlide).trigger('shown');
-      });
-    }
-  })();
-</script>
-
-$for(include-after)$
-$include-after$
-$endfor$
-
-  </body>
-</html>

simulations/03_depvar.R

@@ -73,8 +73,8 @@ parser <- add_argument(parser, "--y_explained_variance", help='what proportion o
 parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.72)
 ## parser <- add_argument(parser, "--x_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
 ## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
-parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.01)
-parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.01)
+parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.3)
+parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.3)
 parser <- add_argument(parser, "--Bzx", help='coeffficient of z on x', default=-0.5)
 parser <- add_argument(parser, "--B0", help='Base rate of y', default=0.5)
 parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")

simulations/03_indep_differential_nonnorm.R

@@ -0,0 +1,185 @@
+### EXAMPLE 1: demonstrates how measurement error can lead to a type sign error in a covariate
+### What kind of data invalidates fong + tyler?
+### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
+### Even when you include the proxy variable in the regression.
+### But with some ground truth and multiple imputation, you can fix it.
+
+library(argparser)
+library(mecor)
+library(ggplot2)
+library(data.table)
+library(filelock)
+library(arrow)
+library(Amelia)
+library(Zelig)
+library(predictionError)
+options(amelia.parallel="no",
+        amelia.ncpus=1)
+setDTthreads(40)
+
+source("simulation_base.R")
+
+## SETUP:
+### we want to estimate x -> y; x is MAR
+### we have x -> k; k -> w; x -> w is used to predict x via the model w.
+### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
+### The labels x are binary, but the model provides a continuous predictor
+
+### simulation:
+#### how much power do we get from the model in the first place? (sweeping N and m)
+#### 
+
+## one way to do it is by adding correlation to x.obs and y that isn't in w.
+## in other words, the model is missing an important feature of x.obs that's related to y.
+simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, y_bias=-0.8,z_bias=0,Px=0.5,accuracy_imbalance_difference=0.3,sd_y_mixin=1){
+    set.seed(seed)
+    # make w and y dependent
+    z <- rnorm(N,sd=0.5)
+    x <- rbinom(N, 1, plogis(Bzx * z + qlogis(Px)))
+    ## following Fong + Tyler: mix y with a Bernoulli(0.15) × |N (0, 20)| to make a skewed non-normal distribution
+    y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bzy*z,Bxy*x)) * ((1-y_explained_variance)/y_explained_variance)
+    y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
+    y <- Bzy * z + Bxy * x + y.epsilon + rbinom(N,1,0.15) * rnorm(N,0,sd_y_mixin)
+    
+    df <- data.table(x=x,y=y,z=z)
+
+    if(m < N){
+        df <- df[sample(nrow(df), m), x.obs := x]
+    } else {
+        df <- df[, x.obs := x]
+    }
+
+    ## probablity of an error is correlated with y
+    ## pz <- mean(z)
+    ## accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
+
+    ## # this works because of conditional probability
+    ## accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
+    ## accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
+
+    ## z0x0 <- df[(z==0) & (x==0)]$x
+    ## z0x1 <- df[(z==0) & (x==1)]$x
+    ## z1x0 <- df[(z==1) & (x==0)]$x
+    ## z1x1 <- df[(z==1) & (x==1)]$x
+
+    ## yz0x0 <- df[(z==0) & (x==0)]$y
+    ## yz0x1 <- df[(z==0) & (x==1)]$y
+    ## yz1x0 <- df[(z==1) & (x==0)]$y
+    ## yz1x1 <- df[(z==1) & (x==1)]$y
+
+    ## nz0x0 <- nrow(df[(z==0) & (x==0)])
+    ## nz0x1 <- nrow(df[(z==0) & (x==1)])
+    ## nz1x0 <- nrow(df[(z==1) & (x==0)])
+    ## nz1x1 <- nrow(df[(z==1) & (x==1)])
+
+    ## yz1 <- df[z==1]$y 
+    ## yz1 <- df[z==1]$y 
+
+    ## # tranform yz0.1 into a logistic distribution with mean accuracy_z0
+    ## acc.z0x0 <- plogis(0.5*scale(yz0x0) + qlogis(accuracy_z0))
+    ## acc.z0x1 <- plogis(0.5*scale(yz0x1) + qlogis(accuracy_z0))
+    ## acc.z1x0 <- plogis(1.5*scale(yz1x0) + qlogis(accuracy_z1))
+    ## acc.z1x1 <- plogis(1.5*scale(yz1x1) + qlogis(accuracy_z1))
+
+    ## w0z0x0 <- (1-z0x0)**2 + (-1)**(1-z0x0) * acc.z0x0
+    ## w0z0x1 <- (1-z0x1)**2 + (-1)**(1-z0x1) * acc.z0x1
+    ## w0z1x0 <- (1-z1x0)**2 + (-1)**(1-z1x0) * acc.z1x0
+    ## w0z1x1 <- (1-z1x1)**2 + (-1)**(1-z1x1) * acc.z1x1
+
+    ## ##perrorz0 <- w0z0*(pyz0)
+    ## ##perrorz1 <- w0z1*(pyz1)
+
+    ## w0z0x0.noisy.odds <- rlogis(nz0x0,qlogis(w0z0x0))
+    ## w0z0x1.noisy.odds <- rlogis(nz0x1,qlogis(w0z0x1))
+    ## w0z1x0.noisy.odds <- rlogis(nz1x0,qlogis(w0z1x0))
+    ## w0z1x1.noisy.odds <- rlogis(nz1x1,qlogis(w0z1x1))
+
+    ## df[(z==0)&(x==0),w:=plogis(w0z0x0.noisy.odds)]
+    ## df[(z==0)&(x==1),w:=plogis(w0z0x1.noisy.odds)]    
+    ## df[(z==1)&(x==0),w:=plogis(w0z1x0.noisy.odds)]    
+    ## df[(z==1)&(x==1),w:=plogis(w0z1x1.noisy.odds)]    
+
+    ## df[,w_pred:=as.integer(w > 0.5)]
+    ## print(mean(df[z==0]$x == df[z==0]$w_pred))
+    ## print(mean(df[z==1]$x == df[z==1]$w_pred))
+    ## print(mean(df$w_pred == df$x))
+
+
+
+    resids <- resid(lm(y~x + z))
+    odds.x1 <- qlogis(prediction_accuracy) + y_bias*qlogis(pnorm(resids[x==1],log.p=T),log.p=T) + z_bias * qlogis(pnorm(z[x==1],sd(z),log.p=T),log.p=T)
+    odds.x0 <- qlogis(prediction_accuracy,lower.tail=F) + y_bias*qlogis(pnorm(resids[x==0],log.p=T),log.p=T) + z_bias * qlogis(pnorm(z[x==0],sd(z),log.p=T),log.p=T)
+
+    ## acc.x0 <- p.correct[df[,x==0]]
+    ## acc.x1 <- p.correct[df[,x==1]]
+
+    df[x==0,w:=plogis(rlogis(.N,odds.x0))]
+    df[x==1,w:=plogis(rlogis(.N,odds.x1))]
+
+    print(prediction_accuracy)
+    print(resids[is.na(df$w)])
+    print(odds.x0[is.na(df$w)])
+    print(odds.x1[is.na(df$w)])
+
+    df[,w_pred := as.integer(w > 0.5)]
+
+
+    print(mean(df$w_pred == df$x))
+    print(mean(df[y>=0]$w_pred == df[y>=0]$x))
+    print(mean(df[y<=0]$w_pred == df[y<=0]$x))
+    return(df)
+}
+
+parser <- arg_parser("Simulate data and fit corrected models")
+parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
+parser <- add_argument(parser, "--seed", default=51, help='seed for the rng')
+parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.1)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.75)
+parser <- add_argument(parser, "--accuracy_imbalance_difference", help='how much more accurate is the predictive model for one class than the other?', default=0.3)
+parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=0.3)
+parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
+parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y*z*x")
+parser <- add_argument(parser, "--y_bias", help='coefficient of y on the probability a classification is correct', default=-0.5)
+parser <- add_argument(parser, "--z_bias", help='coefficient of z on the probability a classification is correct', default=0)
+parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
+parser <- add_argument(parser, "--Px", help='base rate of x', default=0.5)
+parser <- add_argument(parser, "--confint_method", help='method for approximating confidence intervals', default='quad')
+parser <- add_argument(parser, "--sd_y_mixin", help='varience of the non-normal part of Y', default=10)
+args <- parse_args(parser)
+
+B0 <- 0
+Px <- args$Px
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+Bzx <- args$Bzx
+
+if(args$m < args$N){
+
+    df <- simulate_data(args$N, args$m, B0, Bxy, Bzx, Bzy, args$seed, args$y_explained_variance, args$prediction_accuracy, y_bias=args$y_bias, sd_y_mixin=args$sd_y_mixin)
+
+    ## df.pc <- df[,.(x,y,z,w_pred,w)]
+    ##                                     #    df.pc <- df.pc[,err:=x-w_pred]
+    ## pc.df <- pc(suffStat=list(C=cor(df.pc),n=nrow(df.pc)),indepTest=gaussCItest,labels=names(df.pc),alpha=0.05)
+    ## plot(pc.df)
+
+    result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, 'Bzx'=args$Bzx, 'Bzy'=Bzy, 'Px'=Px, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, 'y_bias'=args$y_bias,'outcome_formula'=args$outcome_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, confint_method=args$confint_method, error='', 'sd_y_mixin'=args$sd_y_mixin)
+
+    outline <- run_simulation(df, result, outcome_formula=as.formula(args$outcome_formula), proxy_formula=as.formula(args$proxy_formula), truth_formula=as.formula(args$truth_formula),confint_method=args$confint_method)
+    
+   
+ outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+    if(file.exists(args$outfile)){
+        logdata <- read_feather(args$outfile)
+        logdata <- rbind(logdata,as.data.table(outline), fill=TRUE)
+    } else {
+        logdata <- as.data.table(outline)
+    }
+
+    print(outline)
+    write_feather(logdata, args$outfile)
+    unlock(outfile_lock)
+}

simulations/Makefile

@@ -8,7 +8,7 @@ explained_variances=[0.1]
 
 all:main supplement
 main:remembr.RDS 
-supplement:robustness_1.RDS robustness_1_dv.RDS robustness_2.RDS robustness_2_dv.RDS robustness_3.RDS robustness_3_dv.RDS robustness_3_proflik.RDS robustness_3_dv_proflik.RDS robustness_4.RDS robustness_4_dv.RDS 
+supplement:robustness_1.RDS robustness_1_dv.RDS robustness_2.RDS robustness_2_dv.RDS robustness_3.RDS robustness_3_dv.RDS robustness_3_proflik.RDS robustness_3_dv_proflik.RDS robustness_4.RDS robustness_4_dv.RDS robustness_5.RDS robustness_5_dv.RDS robustness_6.feather
 
 srun=sbatch --wait --verbose run_job.sbatch
 
@@ -16,7 +16,7 @@ srun=sbatch --wait --verbose run_job.sbatch
 joblists:example_1_jobs example_2_jobs example_3_jobs
 
 # test_true_z_jobs: test_true_z.R simulation_base.R
-# 	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript test_true_z.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["test_true_z.feather"], "y_explained_variancevari":${explained_variances}, "Bzx":${Bzx}}' --outfile test_true_z_jobsb
+# 	sbatch --wait --verbose run_job.sbatch  ./grid_sweep.py --command "Rscript test_true_z.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["test_true_z.feather"], "y_explained_variancevari":${explained_variances}, "Bzx":${Bzx}}' --outfile test_true_z_jobsb
 
 # test_true_z.feather: test_true_z_jobs 
 # 	rm -f test_true_z.feather
@@ -25,48 +25,46 @@ joblists:example_1_jobs example_2_jobs example_3_jobs
 
 
 example_1_jobs: 01_two_covariates.R simulation_base.R grid_sweep.py pl_methods.R
-	${srun} grid_sweep.py --command "Rscript 01_two_covariates.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_1.feather"], "y_explained_variance":${explained_variances}, "Bzx":[1]}' --outfile example_1_jobs
+	${srun} ./grid_sweep.py --command "Rscript 01_two_covariates.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_1.feather"], "y_explained_variance":${explained_variances}, "Bzx":[1]}' --outfile example_1_jobs
 
 example_1.feather: example_1_jobs 
 	rm -f example_1.feather
 	sbatch --wait --verbose --array=1-1000  run_simulation.sbatch 0 example_1_jobs
 	sbatch --wait --verbose --array=1001-2000 run_simulation.sbatch 0 example_1_jobs
 	sbatch --wait --verbose --array=2001-3000  run_simulation.sbatch 0 example_1_jobs
-	sbatch --wait --verbose --array=3001-4000  run_simulation.sbatch 0 example_1_jobs
-	sbatch --wait --verbose --array=4001-$(shell cat example_1_jobs | wc -l)  run_simulation.sbatch 0 example_1_jobs
+	sbatch --wait --verbose --array=3001-$(shell cat example_1_jobs | wc -l) run_simulation.sbatch 0 example_1_jobs
 
 example_2_jobs: 02_indep_differential.R simulation_base.R grid_sweep.py pl_methods.R
-	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+z+x"]}' --outfile example_2_jobs
+	sbatch --wait --verbose run_job.sbatch ./grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+z+x"]}' --outfile example_2_jobs
 
 example_2.feather: example_2_jobs 
 	rm -f example_2.feather
 	sbatch --wait --verbose --array=1-1000  run_simulation.sbatch 0 example_2_jobs
 	sbatch --wait --verbose --array=1001-2000 run_simulation.sbatch 0 example_2_jobs
 	sbatch --wait --verbose --array=2001-3000  run_simulation.sbatch 0 example_2_jobs
-	sbatch --wait --verbose --array=3001-4000  run_simulation.sbatch 0 example_2_jobs
-	sbatch --wait --verbose --array=4001-$(shell cat example_2_jobs | wc -l)
+	sbatch --wait --verbose --array=3001-$(shell cat example_2_jobs | wc -l) run_simulation.sbatch 0 example_2_jobs
+
 
 
 # example_2_B_jobs: example_2_B.R
-# 	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript example_2_B.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2_B.feather"]}' --outfile example_2_B_jobs
+# 	sbatch --wait --verbose run_job.sbatch python3 ./grid_sweep.py --command "Rscript example_2_B.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2_B.feather"]}' --outfile example_2_B_jobs
 
 # example_2_B.feather: example_2_B_jobs
 # 	rm -f example_2_B.feather
 # 	sbatch --wait --verbose --array=1-3000 run_simulation.sbatch 0 example_2_B_jobs
 
 example_3_jobs: 03_depvar.R simulation_base.R grid_sweep.py pl_methods.R
-	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript 03_depvar.R" --arg_dict '{"N":${Ns},"m":${ms}, "Bxy":[0.7],"Bzy":[-0.7],"Bzx":[1],"seed":${seeds}, "outfile":["example_3.feather"], "y_explained_variance":${explained_variances}}' --outfile example_3_jobs
+	sbatch --wait --verbose run_job.sbatch ./grid_sweep.py --command "Rscript 03_depvar.R" --arg_dict '{"N":${Ns},"m":${ms}, "Bxy":[0.7],"Bzy":[-0.7],"Bzx":[1],"seed":${seeds}, "outfile":["example_3.feather"], "y_explained_variance":${explained_variances}}' --outfile example_3_jobs
 
 example_3.feather: example_3_jobs
 	rm -f example_3.feather	
 	sbatch --wait --verbose --array=1-1000  run_simulation.sbatch 0 example_3_jobs
 	sbatch --wait --verbose --array=1001-2000 run_simulation.sbatch 0 example_3_jobs
 	 sbatch --wait --verbose --array=2001-3000  run_simulation.sbatch 0 example_3_jobs
-	sbatch --wait --verbose --array=3001-4000  run_simulation.sbatch 0 example_3_jobs
-	sbatch --wait --verbose --array=4001-$(shell cat example_3_jobs | wc -l)  run_simulation.sbatch 0 example_3_jobs
+	sbatch --wait --verbose --array=3001-$(shell cat example_3_jobs | wc -l) run_simulation.sbatch 0 example_3_jobs
 
 example_4_jobs: 04_depvar_differential.R simulation_base.R grid_sweep.py pl_methods.R
-	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript 04_depvar_differential.R" --arg_dict '{"N":${Ns},"Bxy":[0.7],"Bzy":[-0.7],"Bzx":[1], "m":${ms}, "seed":${seeds}, "outfile":["example_4.feather"], "z_bias":[-0.5], "prediction_accuracy":[0.73]}' --outfile example_4_jobs
+	sbatch --wait --verbose run_job.sbatch ./grid_sweep.py --command "Rscript 04_depvar_differential.R" --arg_dict '{"N":${Ns},"Bxy":[0.7],"Bzy":[-0.7],"Bzx":[1], "m":${ms}, "seed":${seeds}, "outfile":["example_4.feather"], "z_bias":[-0.5], "prediction_accuracy":[0.73]}' --outfile example_4_jobs
 
 example_4.feather: example_4_jobs
 	rm -f example_4.feather
@@ -74,9 +72,7 @@ example_4.feather: example_4_jobs
 	sbatch --wait --verbose --array=1001-2000  run_simulation.sbatch 0 example_4_jobs
 	sbatch --wait --verbose --array=2001-3001 run_simulation.sbatch 0 example_4_jobs
 	sbatch --wait --verbose --array=2001-3000  run_simulation.sbatch 0 example_4_jobs
-	sbatch --wait --verbose --array=3001-4000  run_simulation.sbatch 0 example_4_jobs
-	sbatch --wait --verbose --array=4001-$(shell cat example_4_jobs | wc -l)  run_simulation.sbatch 0 example_4_jobs
-
+	sbatch --wait --verbose --array=3001-$(shell cat example_4_jobs | wc -l)  run_simulation.sbatch 0 example_4_jobs
 
 
 remembr.RDS:example_1.feather example_2.feather example_3.feather example_4.feather plot_example.R plot_dv_example.R summarize_estimator.R
@@ -92,22 +88,21 @@ STEP=1000
 ONE=1
 
 robustness_Ns=[1000,5000]
-robustness_robustness_ms=[100,200]
+robustness_ms=[100,200]
 
 #in robustness 1 / example 2 misclassification is correlated with Y.
 robustness_1_jobs_p1: 02_indep_differential.R simulation_base.R grid_sweep.py
-	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":[1000],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3,0],"Bxy":[0.3],"Bzx":[1,0], "outcome_formula":["y~x+z"], "z_bias":[0, 0.5], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~1"]}' --outfile robustness_1_jobs_p1
+	sbatch --wait --verbose run_job.sbatch ./grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":[1000],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3,0],"Bxy":[0.3],"Bzx":[1,0], "outcome_formula":["y~x+z"], "z_bias":[0, 0.5], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~1"]}' --outfile robustness_1_jobs_p1
 
 robustness_1_jobs_p2: 02_indep_differential.R simulation_base.R grid_sweep.py
-	sbatch --wait --verbose run_job.sbatch grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":[5000],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3,0],"Bxy":[0.3],"Bzx":[1,0], "outcome_formula":["y~x+z"], "z_bias":[0, 0.5], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~1"]}' --outfile robustness_1_jobs_p2
+	sbatch --wait --verbose run_job.sbatch ./grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":[5000],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3,0],"Bxy":[0.3],"Bzx":[1,0], "outcome_formula":["y~x+z"], "z_bias":[0, 0.5], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~1"]}' --outfile robustness_1_jobs_p2
 
 robustness_1.feather: robustness_1_jobs_p1 robustness_1_jobs_p2
 	rm -f $@
 	$(eval END_1!=cat robustness_1_jobs_p1 | wc -l)
-	$(eval ITEROBUSTNESS_MS_1!=seq $(START) $(STEP) $(END_1))
+	$(eval ITEMS_1!=seq $(START) $(STEP) $(END_1))
 	$(eval END_2!=cat robustness_1_jobs_p2 | wc -l)
-	$(eval ITEROBUSTNESS_MS_2!=seq $(START) $(STEP) $(END_2))
-
+	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
 	$(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_1_jobs_p1;)
 	$(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_1_jobs_p2;)
 
@@ -117,10 +112,10 @@ robustness_1.RDS: robustness_1.feather summarize_estimator.R
 
 # when Bzy is 0 and zbias is not zero, we have the case where P(W|Y,X,Z) has an omitted variable that is conditionanlly independent from Y.  Note that X and Z are independent in this scenario.
 robustness_1_dv_jobs_p1: simulation_base.R 04_depvar_differential.R grid_sweep.py
-	${srun} grid_sweep.py --command 'Rscript 04_depvar_differential.R' --arg_dict '{"N":[1000],"Bzx":[1], "Bxy":[0.7,0],"Bzy":[-0.7,0],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1_dv.feather"], "proxy_formula":["w_pred~y"],"z_bias":[-0.5]}' --outfile robustness_1_dv_jobs_p1
+	${srun} ./grid_sweep.py --command 'Rscript 04_depvar_differential.R' --arg_dict '{"N":[1000],"Bzx":[1], "Bxy":[0.7,0],"Bzy":[-0.7,0],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1_dv.feather"], "proxy_formula":["w_pred~y"],"z_bias":[-0.5]}' --outfile robustness_1_dv_jobs_p1
 
 robustness_1_dv_jobs_p2: simulation_base.R 04_depvar_differential.R grid_sweep.py
-	${srun} grid_sweep.py --command 'Rscript 04_depvar_differential.R' --arg_dict '{"N":[5000],"Bzx":[1], "Bxy":[0.7,0],"Bzy":[-0.7,0],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1_dv.feather"], "proxy_formula":["w_pred~y"],"z_bias":[-0.5]}' --outfile robustness_1_dv_jobs_p2
+	${srun} ./grid_sweep.py --command 'Rscript 04_depvar_differential.R' --arg_dict '{"N":[5000],"Bzx":[1], "Bxy":[0.7,0],"Bzy":[-0.7,0],"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_1_dv.feather"], "proxy_formula":["w_pred~y"],"z_bias":[-0.5]}' --outfile robustness_1_dv_jobs_p2
 
 robustness_1_dv.feather: robustness_1_dv_jobs_p1 robustness_1_dv_jobs_p2
 	rm -f $@
@@ -136,21 +131,21 @@ robustness_1_dv.RDS: robustness_1_dv.feather summarize_estimator.R
 	${srun} Rscript plot_dv_example.R --infile $< --name "robustness_1_dv" --remember-file $@
 
 
-robustness_2_jobs_p1: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_2_jobs_p1: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.60,0.65]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.60,0.65]}' --outfile $@
 
-robustness_2_jobs_p2: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_2_jobs_p2: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.70,0.75]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.70,0.75]}' --outfile $@
 
-robustness_2_jobs_p3: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_2_jobs_p3: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.80,0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.80,0.85]}' --outfile $@
 
-robustness_2_jobs_p4: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_2_jobs_p4: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.90,0.95]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.90,0.95]}' --outfile $@
 
 robustness_2.feather: robustness_2_jobs_p1 robustness_2_jobs_p2 robustness_2_jobs_p3 robustness_2_jobs_p4
 	rm $@
@@ -172,21 +167,21 @@ robustness_2.RDS: plot_example.R robustness_2.feather summarize_estimator.R
 	rm -f $@
 	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_2" --remember-file $@
 
-robustness_2_dv_jobs_p1: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_2_dv_jobs_p1: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.60,0.65]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.60,0.65]}' --outfile $@
 
-robustness_2_dv_jobs_p2: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_2_dv_jobs_p2: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.70,0.75]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.70,0.75]}' --outfile $@
 
-robustness_2_dv_jobs_p3: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_2_dv_jobs_p3: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.80,0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.80,0.85]}' --outfile $@
 
-robustness_2_dv_jobs_p4: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_2_dv_jobs_p4: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.90,0.95]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_2_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.90,0.95]}' --outfile $@
 
 robustness_2_dv.feather: robustness_2_dv_jobs_p1 robustness_2_dv_jobs_p2 robustness_2_dv_jobs_p3 robustness_2_dv_jobs_p4
 	rm -f $@
@@ -209,9 +204,9 @@ robustness_2_dv.RDS: plot_dv_example.R robustness_2_dv.feather summarize_estimat
 	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_2_dv" --remember-file $@
 
 
-robustness_3_proflik_jobs: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_3_proflik_jobs: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":[1000],"m":[100], "seed":${seeds}, "outfile":["robustness_3_proflik.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.5,0.6,0.7,0.8,0.9,0.95], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85], "confint_method":['spline']}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":[1000],"m":[100], "seed":${seeds}, "outfile":["robustness_3_proflik.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.5,0.6,0.7,0.8,0.9,0.95], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85], "confint_method":['spline']}' --outfile $@
 
 robustness_3_proflik.feather: robustness_3_proflik_jobs
 	rm -f $@
@@ -224,17 +219,17 @@ robustness_3_proflik.RDS: plot_example.R robustness_3_proflik.feather summarize_
 	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_3_proflik" --remember-file $@
 
 
-robustness_3_jobs_p1: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_3_jobs_p1: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.5,0.6], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.5,0.6], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
 
-robustness_3_jobs_p2: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_3_jobs_p2: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.7,0.8], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.7,0.8], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
 
-robustness_3_jobs_p3: grid_sweep.py 01_two_covariates.R simulation_base.R grid_sweep.py
+robustness_3_jobs_p3: grid_sweep.py 01_two_covariates.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.9,0.95], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 01_two_covariates.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"Px":[0.9,0.95], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85]}' --outfile $@
 
 robustness_3.feather: robustness_3_jobs_p1 robustness_3_jobs_p2 robustness_3_jobs_p3
 	rm -f $@
@@ -253,9 +248,9 @@ robustness_3.RDS: plot_example.R robustness_3.feather summarize_estimator.R
 	rm -f $@
 	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_3" --remember-file $@
 
-robustness_3_dv_proflik_jobs: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_3_dv_proflik_jobs: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":[1000],"m":[100], "seed":${seeds}, "outfile":["robustness_3_dv_proflik.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0,0.405,0.846,1.386,2.197,2.944], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"confint_method":['spline']}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":[1000],"m":[100], "seed":${seeds}, "outfile":["robustness_3_dv_proflik.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0,0.405,0.846,1.386,2.197,2.944], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"confint_method":['spline']}' --outfile $@
 
 robustness_3_dv_proflik.feather: robustness_3_dv_proflik_jobs
 	rm -f $@
@@ -268,20 +263,18 @@ robustness_3_dv_proflik.RDS: plot_dv_example.R robustness_3_dv_proflik.feather s
 	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_3_dv_proflik" --remember-file $@
 
 
- robustness_3_dv_jobs_p1: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+ robustness_3_dv_jobs_p1: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0,0.405], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0,0.405], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
 
-
-
-robustness_3_dv_jobs_p2: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_3_dv_jobs_p2: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0.847,1.386], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1],"B0":[0.847,1.386], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
 
 
-robustness_3_dv_jobs_p3: grid_sweep.py 03_depvar.R simulation_base.R grid_sweep.py
+robustness_3_dv_jobs_p3: grid_sweep.py 03_depvar.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "B0":[2.197,2.944], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
+	${srun} ./$< --command 'Rscript 03_depvar.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_3_dv.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "B0":[2.197,2.944], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85]}' --outfile $@
 
 robustness_3_dv.feather: robustness_3_dv_jobs_p1 robustness_3_dv_jobs_p2 robustness_3_dv_jobs_p3
 	rm -f $@
@@ -303,17 +296,22 @@ robustness_3_dv.RDS: plot_dv_example.R robustness_3_dv.feather summarize_estimat
 
 
 
-robustness_4_jobs_p1: grid_sweep.py 02_indep_differential.R simulation_base.R grid_sweep.py
+robustness_4_jobs_p1: grid_sweep.py 02_indep_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 02_indep_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85],"y_bias":[-2.944,-2.197]}' --outfile $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"], "y_bias":[-2.944,-2.197]}' --outfile $@
 
-robustness_4_jobs_p2: grid_sweep.py 02_indep_differential.R simulation_base.R grid_sweep.py
+robustness_4_jobs_p2: grid_sweep.py 02_indep_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 02_indep_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85], "y_bias":[-1.386,-0.846]}' --outfile $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"], "y_bias":[-1.386,-0.846]}' --outfile $@
+
+robustness_4_jobs_p3: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f ./$@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"], "y_bias":[-0.405,-0.25]}' --outfile $@
+
+robustness_4_jobs_p4: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f ./$@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"], "y_bias":[0,-0.1]}' --outfile $@
 
-robustness_4_jobs_p3: grid_sweep.py 02_indep_differential.R simulation_base.R grid_sweep.py
-	rm -f $@
-	${srun} $< --command 'Rscript 02_indep_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~z"], "prediction_accuracy":[0.85],"y_bias":[-0.405,-0.25]}' --outfile $@
 
 robustness_4.feather: robustness_4_jobs_p1 robustness_4_jobs_p2 robustness_4_jobs_p3
 	rm -f $@
@@ -323,10 +321,15 @@ robustness_4.feather: robustness_4_jobs_p1 robustness_4_jobs_p2 robustness_4_job
 	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
 	$(eval END_3!=cat robustness_4_jobs_p3 | wc -l)
 	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
+	$(eval END_4!=cat robustness_4_jobs_p3 | wc -l)
+	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_4))
+
 
 	$(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_jobs_p1;)
 	$(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_jobs_p2;)
 	$(foreach item,$(ITEMS_3),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_jobs_p3;)
+	$(foreach item,$(ITEMS_4),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_jobs_p3;)
+
 
 robustness_4.RDS: plot_example.R robustness_4.feather summarize_estimator.R
 	rm -f $@
@@ -335,34 +338,32 @@ robustness_4.RDS: plot_example.R robustness_4.feather summarize_estimator.R
 
 # '{"N":${robustness_Ns},"Bxy":[0.7],"Bzy":[-0.7],"m":${ms}, "seed":${seeds}, "outfile":["example_4.feather"], "z_bias":[0.5]}' --example_4_jobs
 
-robustness_4_dv_jobs_p1: grid_sweep.py 04_depvar_differential.R simulation_base.R grid_sweep.py
+robustness_4_dv_jobs_p1: grid_sweep.py 04_depvar_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"z_bias":[0,0.1]}' --outfile $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "z_bias":[0,0.1]}' --outfile $@
 
-robustness_4_dv_jobs_p2: grid_sweep.py 04_depvar_differential.R simulation_base.R grid_sweep.py
+robustness_4_dv_jobs_p2: grid_sweep.py 04_depvar_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"z_bias":[0.25,0.405]}' --outfile $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "z_bias":[0.25,0.405]}' --outfile $@
 
-robustness_4_dv_jobs_p3: grid_sweep.py 04_depvar_differential.R simulation_base.R grid_sweep.py
+robustness_4_dv_jobs_p3: grid_sweep.py 04_depvar_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1],"outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"z_bias":[0.846,1.386]}' --outfile $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1],"outcome_formula":["y~x+z"],"z_bias":[0.846,1.386]}' --outfile $@ 
 
-robustness_4_dv_jobs_p4: grid_sweep.py 04_depvar_differential.R simulation_base.R grid_sweep.py
+robustness_4_dv_jobs_p4: grid_sweep.py 04_depvar_differential.R simulation_base.R
 	rm -f $@
-	${srun} $< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"],"Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "prediction_accuracy":[0.85],"z_bias":[2.197,2.944]}' --outfile $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_4_dv.feather"],"Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1], "outcome_formula":["y~x+z"], "z_bias":[2.197,2.944]}' --outfile $@
 
 robustness_4_dv.feather: robustness_4_dv_jobs_p1 robustness_4_dv_jobs_p2 robustness_4_dv_jobs_p3 robustness_4_dv_jobs_p4
 	rm -f $@
 	$(eval END_1!=cat robustness_4_dv_jobs_p1 | wc -l)
 	$(eval ITEMS_1!=seq $(START) $(STEP) $(END_1))
-	$(eval END_2!=cat robustness_4_dv_p2 | wc -l)
+	$(eval END_2!=cat robustness_4_dv_jobs_p2 | wc -l)
 	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
-	$(eval END_3!=cat robustness_4_dv_p3 | wc -l)
+	$(eval END_3!=cat robustness_4_dv_jobs_p3 | wc -l)
 	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
-	$(eval END_3!=cat robustness_4_dv_p4 | wc -l)
-	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
-
-
+	$(eval END_4!=cat robustness_4_dv_jobs_p4 | wc -l)
+	$(eval ITEMS_4!=seq $(START) $(STEP) $(END_4))
 	$(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_dv_jobs_p1;)
 	$(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_dv_jobs_p2;)
 	$(foreach item,$(ITEMS_3),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_4_dv_jobs_p3;)
@@ -371,7 +372,86 @@ robustness_4_dv.feather: robustness_4_dv_jobs_p1 robustness_4_dv_jobs_p2 robustn
 
 robustness_4_dv.RDS: plot_dv_example.R robustness_4_dv.feather summarize_estimator.R
 	rm -f $@
-	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_4" --remember-file $@
+	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_4_dv" --remember-file $@
+
+
+robustness_5_jobs_p1: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[1.386,2.197], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"]}' --outfile $@
+
+robustness_5_jobs_p2: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[0.405,0.846], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"]}' --outfile $@
+
+robustness_5_jobs_p3: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[0,0.25], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"]}' --outfile $@
+
+robustness_5_jobs_p4: grid_sweep.py 02_indep_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 02_indep_differential.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[2.944], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"]}' --outfile $@
+
+
+robustness_5.feather: robustness_5_jobs_p1 robustness_5_jobs_p2 robustness_5_jobs_p3
+	rm -f $@
+	$(eval END_1!=cat robustness_5_jobs_p1 | wc -l)
+	$(eval ITEMS_1!=seq $(START) $(STEP) $(END_1))
+	$(eval END_2!=cat robustness_5_jobs_p2 | wc -l)
+	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
+	$(eval END_3!=cat robustness_5_jobs_p3 | wc -l)
+	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
+	$(eval END_4!=cat robustness_5_jobs_p4 | wc -l)
+	$(eval ITEMS_4!=seq $(START) $(STEP) $(END_4))
+
+	$(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_jobs_p1;)
+	$(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_jobs_p2;)
+	$(foreach item,$(ITEMS_3),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_jobs_p3;)
+	$(foreach item,$(ITEMS_4),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_jobs_p4;)
+
+robustness_5.RDS: plot_example.R robustness_5.feather summarize_estimator.R
+	rm -f $@
+	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_5" --remember-file $@
+
+
+# '{"N":${robustness_Ns},"Bxy":[0.7],"Bzy":[-0.7],"m":${ms}, "seed":${seeds}, "outfile":["example_4.feather"], "z_bias":[0.5]}' --example_4_jobs
+
+robustness_5_dv_jobs_p1: grid_sweep.py 04_depvar_differential.R simulation_base.R
+	rm -f $@
+	 ${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[0,0.25], "outcome_formula":["y~x+z"], "z_bias":[-0.5]}' --outfile $@
+
+robustness_5_dv_jobs_p2: grid_sweep.py 04_depvar_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[0.405,0.846], "outcome_formula":["y~x+z"],  "z_bias":[-0.5]}' --outfile $@
+
+robustness_5_dv_jobs_p3: grid_sweep.py 04_depvar_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5_dv.feather"], "Bzy":[-0.7],"Bxy":[0.7],"Bzx":[1.386,2.197],"outcome_formula":["y~x+z"], "z_bias":[-0.5]}' --outfile $@ 
+
+robustness_5_dv_jobs_p4: grid_sweep.py 04_depvar_differential.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 04_depvar_differential.R'  --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_5_dv.feather"],"Bzy":[-0.7],"Bxy":[0.7],"Bzx":[2.944], "outcome_formula":["y~x+z"], "z_bias":[-0.5]}' --outfile $@
+
+robustness_5_dv.feather: robustness_5_dv_jobs_p1 robustness_5_dv_jobs_p2 robustness_5_dv_jobs_p3 robustness_5_dv_jobs_p4
+	rm -f $@
+	$(eval END_1!=cat robustness_5_dv_jobs_p1 | wc -l)
+	$(eval ITEMS_1!=seq $(START) $(STEP) $(END_1))
+	$(eval END_2!=cat robustness_5_dv_jobs_p2 | wc -l)
+	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
+	$(eval END_3!=cat robustness_5_dv_jobs_p3 | wc -l)
+	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
+	$(eval END_4!=cat robustness_5_dv_jobs_p4 | wc -l)
+	$(eval ITEMS_4!=seq $(START) $(STEP) $(END_4))
+
+
+	$(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_dv_jobs_p1;)
+	$(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_dv_jobs_p2;)
+	$(foreach item,$(ITEMS_3),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_dv_jobs_p3;)
+	$(foreach item,$(ITEMS_4),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_5_dv_jobs_p4;)
+
+
+robustness_5_dv.RDS: plot_dv_example.R robustness_5_dv.feather summarize_estimator.R
+	rm -f $@
+	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_5_dv" --remember-file $@
 
 
 clean_main:
@@ -404,5 +484,44 @@ clean_all:
 # 	sbatch --wait --verbose --array=1-3000 run_simulation.sbatch 0 example_2_B_mecor_jobs
 # 	sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_2_B_mecor_jobs
 
+robustness_6_jobs_p1: grid_sweep.py 03_indep_differential_nonnorm.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 03_indep_differential_nonnorm.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_6.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"],"sd_y_mixin":[0,1,2.5]}' --outfile $@
+
+robustness_6_jobs_p2: grid_sweep.py 03_indep_differential_nonnorm.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 03_indep_differential_nonnorm.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_6.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"],"sd_y_mixin":[5,10]}' --outfile $@
+
+robustness_6_jobs_p3: grid_sweep.py 03_indep_differential_nonnorm.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 03_indep_differential_nonnorm.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_6.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"],"sd_y_mixin":[0,1,2.5],"y_bias":[0]}' --outfile $@
+
+robustness_6_jobs_p4: grid_sweep.py 03_indep_differential_nonnorm.R simulation_base.R
+	rm -f $@
+	${srun} ./$< --command 'Rscript 03_indep_differential_nonnorm.R' --arg_dict '{"N":${robustness_Ns},"m":${robustness_ms}, "seed":${seeds}, "outfile":["robustness_6.feather"],"y_explained_variance":${explained_variances}, "Bzy":[-0.3],"Bxy":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x+z"], "truth_formula":["x~z"],"sd_y_mixin":[5,10],"y_bias":[0]}' --outfile $@
+
+
+robustness_6.feather: robustness_6_jobs_p1 robustness_6_jobs_p2 robustness_6_jobs_p3 robustness_6_jobs_p4
+	rm -f $@
+	$(eval END_1!=cat robustness_6_jobs_p1 | wc -l)
+	$(eval ITEMS_1!=seq $(START) $(STEP) $(END_1))
+	$(eval END_2!=cat robustness_6_jobs_p2 | wc -l)
+	$(eval ITEMS_2!=seq $(START) $(STEP) $(END_2))
+	$(eval END_3!=cat robustness_6_jobs_p3 | wc -l)
+	$(eval ITEMS_3!=seq $(START) $(STEP) $(END_3))
+	$(eval END_4!=cat robustness_6_jobs_p4 | wc -l)
+	$(eval ITEMS_4!=seq $(START) $(STEP) $(END_4))
+
+
+	# $(foreach item,$(ITEMS_1),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_6_jobs_p1;)
+	# $(foreach item,$(ITEMS_2),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_6_jobs_p2;)
+	# $(foreach item,$(ITEMS_3),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_6_jobs_p3;)
+	$(foreach item,$(ITEMS_4),sbatch --wait --verbose --array=$(shell expr $(item) + $(ONE))-$(shell expr $(item) + $(STEP)) run_simulation.sbatch 0 robustness_6_jobs_p4;)
+
+
+robustness_6.RDS: plot_example.R robustness_6.feather summarize_estimator.R
+	rm -f $@
+	${srun} Rscript $< --infile $(word 2, $^) --name "robustness_6" --remember-file $@
+
 
 .PHONY: supplement

simulations/grid_sweep.py

@@ -8,6 +8,8 @@ def main(command, arg_dict, outfile, remember_file='remember_grid_sweep.RDS'):
     print(remember_file)
     remember = pyRemembeR.remember.Remember()
     remember.set_file(remember_file)
+    if type(arg_dict) is not dict:
+        arg_dict = eval(arg_dict)
     remember[outfile] = arg_dict
     remember.save_to_r()
     keys = []

simulations/measerr_methods.R

@@ -23,7 +23,7 @@ likelihood.logistic <- function(model.params, outcome, model.matrix){
 }
 
 ## outcome_formula <- y ~ x + z; proxy_formula <- w_pred ~ y + x + z + x:z + x:y + z:y 
-measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='logit'), proxy_formula, proxy_family=binomial(link='logit'),method='optim'){
+measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='logit'), proxy_formula, proxy_family=binomial(link='logit'),maxit=1e6, method='optim',optim_method='L-BFGS-B'){
     df.obs <- model.frame(outcome_formula, df)
     proxy.model.matrix <- model.matrix(proxy_formula, df)
     proxy.variable <- all.vars(proxy_formula)[1]
@@ -106,7 +106,7 @@ measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='lo
     names(start) <- params
     
     if(method=='optim'){
-        fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
+        fit <- optim(start, fn = nll, lower=lower, method=optim_method, hessian=TRUE, control=list(maxit=maxit))
     } else {
         quoted.names <- gsub("[\\(\\)]",'',names(start))
         print(quoted.names)
@@ -115,13 +115,13 @@ measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='lo
         measerr_mle_nll <- eval(parse(text=text))
         names(start) <- quoted.names
         names(lower) <- quoted.names
-        fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
+        fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, parnames=params,control=list(maxit=maxit),method=optim_method)
     }
     return(fit)
 }
 
 
-measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit'),method='optim'){
+measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit'),method='optim', maxit=1e6, optim_method='L-BFGS-B'){
 
     df.obs <- model.frame(outcome_formula, df)
     response.var <- all.vars(outcome_formula)[1]
@@ -240,7 +240,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
     names(start) <- params
 
     if(method=='optim'){
-        fit <- optim(start, fn = measerr_mle_nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
+        fit <- optim(start, fn = measerr_mle_nll, lower=lower, method=optim_method, hessian=TRUE, control=list(maxit=maxit))
     } else { # method='mle2'
                 
         quoted.names <- gsub("[\\(\\)]",'',names(start))
@@ -250,7 +250,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
         measerr_mle_nll_mle <- eval(parse(text=text))
         names(start) <- quoted.names
         names(lower) <- quoted.names
-        fit <- mle2(minuslogl=measerr_mle_nll_mle, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
+        fit <- mle2(minuslogl=measerr_mle_nll_mle, start=start, lower=lower, parnames=params,control=list(maxit=maxit),method=optim_method)
     }
 
     return(fit)

simulations/pl_methods.R

@@ -51,19 +51,20 @@ zhang.mle.iv <- function(df){
     fn <- df.obs[(w_pred==0) & (x.obs==1), .N]
     npv <- tn / (tn + fn)
 
+
     tp <- df.obs[(w_pred==1) & (x.obs == w_pred),.N]
     fp <- df.obs[(w_pred==1) & (x.obs == 0),.N]
     ppv <- tp / (tp + fp)
 
-    nll <- function(B0=0, Bxy=0, Bzy=0, sigma_y=0.1){
+    nll <- function(B0=0, Bxy=0, Bzy=0, sigma_y=9){
 
     ## fpr = 1 - TNR
     ### Problem: accounting for uncertainty in ppv / npv
 
     ## fnr = 1 - TPR
     ll.y.obs <- with(df.obs, dnorm(y, B0 + Bxy * x + Bzy * z, sd=sigma_y,log=T))
+
     ll <- sum(ll.y.obs)
-    
     # unobserved case; integrate out x
     ll.x.1 <- with(df.unobs, dnorm(y, B0 + Bxy + Bzy * z, sd = sigma_y, log=T))
     ll.x.0 <- with(df.unobs, dnorm(y, B0 + Bzy * z, sd = sigma_y,log=T))
@@ -75,10 +76,11 @@ zhang.mle.iv <- function(df){
     lls.x.0 <- colLogSumExps(rbind(log(1-npv) + ll.x.1, log(npv) + ll.x.0))
 
     lls <- colLogSumExps(rbind(df.unobs$w_pred * lls.x.1, (1-df.unobs$w_pred) * lls.x.0))
+        
     ll <- ll + sum(lls)
-    return(-ll)
+
     }    
-    mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6), lower=list(sigma_y=0.0001, B0=-Inf, Bxy=-Inf, Bzy=-Inf),
+    mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6), lower=list(sigma_y=0.00001, B0=-Inf, Bxy=-Inf, Bzy=-Inf),
                    upper=list(sigma_y=Inf, B0=Inf, Bxy=Inf, Bzy=Inf),method='L-BFGS-B')
     return(mlefit)
 }

simulations/plot_dv_example.R

@@ -94,6 +94,7 @@ set.remember.prefix(gsub("plot.df.","",args$name))
 
 remember(median(sims.df$cor.xz),'med.cor.xz')
 remember(median(sims.df$accuracy),'med.accuracy')
+remember(mean(sims.df$accuracy),'mean.accuracy')
 remember(median(sims.df$error.cor.x),'med.error.cor.x')
 remember(median(sims.df$error.cor.z),'med.error.cor.z')
 remember(median(sims.df$lik.ratio),'med.lik.ratio')

simulations/run_job.sbatch

@@ -9,7 +9,6 @@
 #SBATCH --time=4:00:00
 ## Memory per node
 #SBATCH --mem=4G
-#SBATCH --cpus-per-task=1
 #SBATCH --ntasks-per-node=1
 #SBATCH --chdir /gscratch/comdata/users/nathante/ml_measurement_error_public/simulations
 #SBATCH --output=simulation_jobs/%A_%a.out

simulations/simulation_base.R

@@ -151,21 +151,11 @@ run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formu
     temp.df <- copy(df)
     temp.df[,y:=y.obs]
 
-    if(confint_method=='quad'){
-        mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
-        fischer.info <- solve(mod.caroll.lik$hessian)
-        coef <- mod.caroll.lik$par
-        ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
-        ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
-    }
-    else{ ## confint_method is 'profile'
-
-        mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, method='bbmle')
-        coef <- coef(mod.caroll.lik)
-        ci <- confint(mod.caroll.lik, method='spline')
-        ci.lower <- ci[,'2.5 %']
-        ci.upper <- ci[,'97.5 %']
-    }
+    mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+    fischer.info <- solve(mod.caroll.lik$hessian)
+    coef <- mod.caroll.lik$par
+    ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
+    ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 
     result <- append(result,
                      list(Bxy.est.mle = coef['x'],
@@ -175,6 +165,19 @@ run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formu
                           Bzy.ci.upper.mle = ci.upper['z'],
                           Bzy.ci.lower.mle = ci.lower['z']))
 
+    mod.caroll.profile.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, method='bbmle')
+    coef <- coef(mod.caroll.profile.lik)
+    ci <- confint(mod.caroll.profile.lik, method='spline')
+    ci.lower <- ci[,'2.5 %']
+    ci.upper <- ci[,'97.5 %']
+
+    result <- append(result,
+                     list(Bxy.est.mle.profile = coef['x'],
+                          Bxy.ci.upper.mle.profile = ci.upper['x'],
+                          Bxy.ci.lower.mle.profile = ci.lower['x'],
+                          Bzy.est.mle.profile = coef['z'],
+                          Bzy.ci.upper.mle.profile = ci.upper['z'],
+                          Bzy.ci.lower.mle.profile = ci.lower['z']))
 
     ## my implementatoin of liklihood based correction
     mod.zhang <- zhang.mle.dv(df)
@@ -201,8 +204,8 @@ run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formu
                           )
 
     tryCatch({
-        amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
-        mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+        amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'),ords="y.obs")
+        mod.amelia.k <- zelig(y.obs~x+z, model='logit', data=amelia.out.k$imputations, cite=FALSE)
         (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
         est.x.mi <- coefse['x','Estimate']
         est.x.se <- coefse['x','Std.Error']
@@ -340,44 +343,72 @@ run_simulation <-  function(df, result, outcome_formula=y~x+z, proxy_formula=NUL
     tryCatch({
         temp.df <- copy(df)
         temp.df <- temp.df[,x:=x.obs]
-        if(confint_method=='quad'){
-            mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='optim')
-            fischer.info <- solve(mod.caroll.lik$hessian)
-            coef <- mod.caroll.lik$par
-            ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
-            ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
-        } else { # confint_method == 'bbmle'
+        mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='optim')
+        fischer.info <- solve(mod.caroll.lik$hessian)
+        coef <- mod.caroll.lik$par
+        ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
+        ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 
-            mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='bbmle')
-            coef <- coef(mod.caroll.lik)
-            ci <- confint(mod.caroll.lik, method='spline')
-            ci.lower <- ci[,'2.5 %']
-            ci.upper <- ci[,'97.5 %']
-        }
         mle_result <- list(Bxy.est.mle = coef['x'],
                            Bxy.ci.upper.mle = ci.upper['x'],
                            Bxy.ci.lower.mle = ci.lower['x'],
                            Bzy.est.mle = coef['z'],
                            Bzy.ci.upper.mle = ci.upper['z'],
                            Bzy.ci.lower.mle = ci.lower['z'])
+        },
+        error=function(e) {result[['error']] <- as.character(e)
+        })
+
+    result <- append(result, mle_result)
+    mle_result_proflik <- list(Bxy.est.mle.profile = NULL,
+                               Bxy.ci.upper.mle.profile = NULL,
+                               Bxy.ci.lower.mle.profile = NULL,
+                               Bzy.est.mle.profile = NULL,
+                               Bzy.ci.upper.mle.profile = NULL,
+                               Bzy.ci.lower.mle.profile = NULL)
+
+    tryCatch({
+        ## confint_method == 'bbmle'
+        mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='bbmle')
+        coef <- coef(mod.caroll.lik)
+        ci <- confint(mod.caroll.lik, method='spline')
+        ci.lower <- ci[,'2.5 %']
+        ci.upper <- ci[,'97.5 %']
+
+        mle_result_proflik <- list(Bxy.est.mle.profile = coef['x'],
+                                   Bxy.ci.upper.mle.profile = ci.upper['x'],
+                                   Bxy.ci.lower.mle.profile = ci.lower['x'],
+                                   Bzy.est.mle.profile = coef['z'],
+                                   Bzy.ci.upper.mle.profile = ci.upper['z'],
+                                   Bzy.ci.lower.mle.profile = ci.lower['z'])
     },
 
     error=function(e) {result[['error']] <- as.character(e)
     })
-
         
-    result <- append(result, mle_result)
+    result <- append(result, mle_result_proflik)
 
+    zhang_result <- list(Bxy.est.mle.zhang = NULL,
+                       Bxy.ci.upper.mle.zhang = NULL,
+                       Bxy.ci.lower.mle.zhang = NULL,
+                       Bzy.est.mle.zhang = NULL,
+                       Bzy.ci.upper.mle.zhang = NULL,
+                       Bzy.ci.lower.mle.zhang = NULL)
+
+    tryCatch({
     mod.zhang.lik <- zhang.mle.iv(df)
     coef <- coef(mod.zhang.lik)
     ci <- confint(mod.zhang.lik,method='quad')
-    result <- append(result,
-                     list(Bxy.est.zhang = coef['Bxy'],
-                          Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
-                          Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
-                          Bzy.est.zhang = coef['Bzy'],
-                          Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
-                          Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
+    zhang_result <- list(Bxy.est.zhang = coef['Bxy'],
+                         Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
+                         Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
+                         Bzy.est.zhang = coef['Bzy'],
+                         Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
+                         Bzy.ci.lower.zhang = ci['Bzy','2.5 %'])
+    },
+    error=function(e) {result[['error']] <- as.character(e)
+    })
+    result <- append(result, zhang_result)
 
     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
     ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)

simulations/summarize_estimator.R

@@ -1,5 +1,6 @@
+library(ggdist)
 
-summarize.estimator <- function(df, suffix='naive', coefname='x'){
+summarize.estimator <- function(sims.df, suffix='naive', coefname='x'){
 
     reported_vars <- c(
                        'Bxy',
@@ -13,10 +14,10 @@ summarize.estimator <- function(df, suffix='naive', coefname='x'){
 
     grouping_vars <- grouping_vars[grouping_vars %in% names(df)]
 
-    part <- df[,
-               c(reported_vars,
-                 grouping_vars),
-               with=FALSE]
+    part <- sims.df[,
+                    unique(c(reported_vars,
+                             grouping_vars)),
+                    with=FALSE]
 
 
     true.in.ci <- as.integer((part$Bxy >= part[[paste0('B',coefname,'y.ci.lower.',suffix)]]) & (part$Bxy <= part[[paste0('B',coefname,'y.ci.upper.',suffix)]]))
@@ -29,6 +30,7 @@ summarize.estimator <- function(df, suffix='naive', coefname='x'){
                        bias=bias,
                        sign.correct =sign.correct)]
 
+
     part.plot <- part[, .(p.true.in.ci = mean(true.in.ci),
                           mean.bias = mean(bias),
                           mean.est = mean(.SD[[paste0('B',coefname,'y.est.',suffix)]],na.rm=T),