cleaning up + implementing robustness checks

+ add pl_methods.R
+ update makefile
+ fix bug in 02_indep_differential.R
+ start documenting robustness checks in robustness_check_notes.md

simulations/02_indep_differential.R

@@ -104,9 +104,10 @@ simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.
     ## 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])) + z_bias * qlogis(pnorm(z,sd(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,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]]

simulations/Makefile

@@ -120,12 +120,10 @@ remember_irr.RDS: example_5.feather plot_irr_example.R plot_irr_dv_example.R sum
 #	sbatch --wait --verbose run_job.sbatch Rscript plot_irr_dv_example.R --infile example_6.feather --name "plot.df.example.6"
 
 
-
 robustness_1_jobs: 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":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["robustness_1.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y+x"], "truth_formula":["x~1"]}' --outfile robustness_1_jobs
 
 
-
 robustness_1.feather: robustness_1_jobs
 	rm -f robustness_1.feather
 	sbatch --wait --verbose --array=1-$(shell cat robustness_1_jobs | wc -l)  run_simulation.sbatch 0 robustness_1_jobs

simulations/pl_methods.R

@@ -0,0 +1,84 @@
+library(stats4)
+library(bbmle)
+library(matrixStats)
+
+zhang.mle.dv <- function(df){
+    df.obs <- df[!is.na(y.obs)]
+    df.unobs <- df[is.na(y.obs)]
+
+    fp <- df.obs[(w_pred==1) & (y.obs != w_pred),.N]
+    tn <- df.obs[(w_pred == 0) & (y.obs == w_pred),.N]
+    fpr <- fp / (fp+tn)
+
+    fn <- df.obs[(w_pred==0) & (y.obs != w_pred), .N]
+    tp <- df.obs[(w_pred==1) & (y.obs == w_pred),.N]
+    fnr <- fn / (fn+tp)
+
+    nll <- function(B0=0, Bxy=0, Bzy=0){
+
+
+        ## observed case
+        ll.y.obs <- vector(mode='numeric', length=nrow(df.obs))
+        ll.y.obs[df.obs$y.obs==1] <- with(df.obs[y.obs==1], plogis(B0 + Bxy * x + Bzy * z,log=T))
+        ll.y.obs[df.obs$y.obs==0] <- with(df.obs[y.obs==0], plogis(B0 + Bxy * x + Bzy * z,log=T,lower.tail=FALSE))
+
+        ll <- sum(ll.y.obs)
+
+        pi.y.1 <- with(df.unobs,plogis(B0 + Bxy * x + Bzy*z, log=T))
+        #pi.y.0 <- with(df.unobs,plogis(B0 + Bxy * x + Bzy*z, log=T,lower.tail=FALSE))
+
+        lls <- with(df.unobs, colLogSumExps(rbind(w_pred * colLogSumExps(rbind(log(fpr), log(1 - fnr - fpr)+pi.y.1)),
+        (1-w_pred) * (log(1-fpr) - exp(log(1-fnr-fpr)+pi.y.1)))))
+    
+        ll <- ll + sum(lls)
+        print(paste0(B0,Bxy,Bzy))
+        print(ll)
+        return(-ll)
+    }    
+    mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6),method='L-BFGS-B',lower=c(B0=-Inf, Bxy=-Inf, Bzy=-Inf),
+                   upper=c(B0=Inf, Bxy=Inf, Bzy=Inf))
+    return(mlefit)
+}
+
+
+## model from Zhang's arxiv paper, with predictions for y
+## Zhang got this model from Hausman 1998
+zhang.mle.iv <- function(df){
+    df.obs <- df[!is.na(x.obs)]
+    df.unobs <- df[is.na(x.obs)]
+
+    tn <- df.obs[(w_pred == 0) & (x.obs == w_pred),.N]
+    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){
+
+    ## 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))
+
+    ## case x == 1
+    lls.x.1 <- colLogSumExps(rbind(log(ppv) + ll.x.1, log(1-ppv) + ll.x.0))
+    
+    ## case x == 0
+    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),
+                   upper=list(sigma_y=Inf, B0=Inf, Bxy=Inf, Bzy=Inf),method='L-BFGS-B')
+    return(mlefit)
+}

simulations/robustness_check_notes.md

@@ -0,0 +1,5 @@
+# robustness_1.RDS
+
+Tests how robust the MLE method is when the model for $X$ is less precise. In the main result, we include $Z$ on the right-hand-side of the `truth_formula`. 
+In this robustness check, the `truth_formula` is an intercept-only model.
+