277 lines
11 KiB
R
277 lines
11 KiB
R
### EXAMPLE 2_b: demonstrates how measurement error can lead to a type sign error in a covariate
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### This is the same as example 2, only instead of x->k we have k->x.
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### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
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### Even when you include the proxy variable in the regression.
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### But with some ground truth and multiple imputation, you can fix it.
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library(argparser)
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library(mecor)
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library(ggplot2)
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library(data.table)
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library(filelock)
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library(arrow)
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library(Amelia)
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library(Zelig)
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library(predictionError)
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options(amelia.parallel="no",
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amelia.ncpus=1)
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source("simulation_base.R")
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## SETUP:
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### we want to estimate x -> y; x is MAR
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### we have x -> k; k -> w; x -> w is used to predict x via the model w.
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### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
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### The labels x are binary, but the model provides a continuous predictor
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### simulation:
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#### how much power do we get from the model in the first place? (sweeping N and m)
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####
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logistic <- function(x) {1/(1+exp(-1*x))}
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simulate_latent_cocause <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
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set.seed(seed)
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## the true value of x
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g <- rbinom(N, 1, 0.5)
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xprime <- Bgx * g + rnorm(N,0,1)
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k <- Bkx*xprime + rnorm(N,0,3)
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x <- as.integer(logistic(scale(xprime)) > 0.5)
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y <- Bxy * x + Bgy * g + rnorm(N, 0, 2) + B0
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df <- data.table(x=x,k=k,y=y,g=g)
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if( m < N){
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df <- df[sample(nrow(df), m), x.obs := x]
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} else {
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df <- df[, x.obs := x]
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}
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w.model <- glm(x ~ k,df, family=binomial(link='logit'))
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w <- predict(w.model,data.frame(k=k)) + rnorm(N,0,1)
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## y = B0 + B1x + e
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df[,':='(w=w, w_pred = as.integer(w>0.5))]
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return(df)
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}
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schennach <- function(df){
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fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
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df[,xstar_pred := predict(fwx, df)]
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gxt <- lm(y ~ xstar_pred+g, df)
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}
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parser <- arg_parser("Simulate data and fit corrected models")
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parser <- add_argument(parser, "--N", default=100, help="number of observations of w")
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parser <- add_argument(parser, "--m", default=20, help="m the number of ground truth observations")
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parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng')
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parser <- add_argument(parser, "--outfile", help='output file', default='example_2_B.feather')
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args <- parse_args(parser)
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rows <- list()
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B0 <- 0
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Bxy <- 0.2
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Bgy <- -0.2
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Bkx <- 1
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Bgx <- 3
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outline <- run_simulation(simulate_latent_cocause(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
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,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))
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outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
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if(file.exists(args$outfile)){
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logdata <- read_feather(args$outfile)
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logdata <- rbind(logdata,as.data.table(outline))
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} else {
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logdata <- as.data.table(outline)
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}
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print(outline)
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write_feather(logdata, args$outfile)
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unlock(outfile_lock)
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## Ns <- c(1e6, 5e4, 1000)
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## ms <- c(100, 250, 500, 1000)
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## seeds <- 1:500
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## rowssets <- list()
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## library(doParallel)
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## options(mc.cores = parallel::detectCores())
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## cl <- makeCluster(20)
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## registerDoParallel(cl)
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## ## library(future)
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## ## plan(multiprocess,workers=40,gc=TRUE)
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## for(N in Ns){
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## print(N)
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## for(m in ms){
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## if(N>m){
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## new.rows <- foreach(iter=seeds, .combine=rbind, .packages = c('mecor','Amelia','Zelig','predictionError','data.table'),
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## .export = c("run_simulation","simulate_latent_cocause","logistic","N","m","B0","Bxy","Bgy","Bkx","Bgx")) %dopar%
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## {run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, iter)
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## ,list('N'=N,'m'=m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=iter))}
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## rowsets <- append(rowssets, list(data.table(new.rows)))
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## }
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## }
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## ## rows <- append(rows, list(future({run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)
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## }
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## ,list(N=N,m=m,B0=B0,Bxy=Bxy,Bgy=Bgy, Bkx=Bkx, Bgx=Bgx, seed=seed))w},
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## packages=c('mecor','Amelia','Zelig','predictionError'),
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## seed=TRUE)))
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## df <- rbindlist(rowsets)
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## write_feather(df,"example_2B_simulation.feather")
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## run_simulation <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
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## result <- list()
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## df <- simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)
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## result <- append(result, list(N=N,
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## m=m,
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## B0=B0,
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## Bxy=Bxy,
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## Bgy=Bgy,
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## Bkx=Bkx,
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## seed=seed))
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## (accuracy <- df[,.(mean(w_pred==x))])
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## result <- append(result, list(accuracy=accuracy))
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## (model.true <- lm(y ~ x + g, data=df))
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## true.ci.Bxy <- confint(model.true)['x',]
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## true.ci.Bgy <- confint(model.true)['g',]
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## result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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## Bgy.est.true=coef(model.true)['g'],
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## Bxy.ci.upper.true = true.ci.Bxy[2],
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## Bxy.ci.lower.true = true.ci.Bxy[1],
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## Bgy.ci.upper.true = true.ci.Bgy[2],
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## Bgy.ci.lower.true = true.ci.Bgy[1]))
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## (model.feasible <- lm(y~x.obs+g,data=df))
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## feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
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## result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
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## Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
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## Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
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## feasible.ci.Bgy <- confint(model.feasible)['g',]
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## result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
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## Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
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## Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
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## (model.naive <- lm(y~w+g, data=df))
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## naive.ci.Bxy <- confint(model.naive)['w',]
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## naive.ci.Bgy <- confint(model.naive)['g',]
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## result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
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## Bgy.est.naive=coef(model.naive)['g'],
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## Bxy.ci.upper.naive = naive.ci.Bxy[2],
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## Bxy.ci.lower.naive = naive.ci.Bxy[1],
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## Bgy.ci.upper.naive = naive.ci.Bgy[2],
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## Bgy.ci.lower.naive = naive.ci.Bgy[1]))
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## ## multiple imputation when k is observed
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## ## amelia does great at this one.
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## amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=c("x.obs","g"),lgstc=c('w'))
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## mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
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## (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
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## est.x.mi <- coefse['x.obs','Estimate']
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## est.x.se <- coefse['x.obs','Std.Error']
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## result <- append(result,
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## list(Bxy.est.amelia.full = est.x.mi,
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## Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
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## Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
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## ))
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## est.g.mi <- coefse['g','Estimate']
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## est.g.se <- coefse['g','Std.Error']
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## result <- append(result,
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## list(Bgy.est.amelia.full = est.g.mi,
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## Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
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## Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
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## ))
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## ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
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## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","k"), noms=c("x.obs",'g'),lgstc = c("w"))
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## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
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## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
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## est.x.mi <- coefse['x.obs','Estimate']
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## est.x.se <- coefse['x.obs','Std.Error']
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## result <- append(result,
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## list(Bxy.est.amelia.nok = est.x.mi,
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## Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
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## Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
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## ))
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## est.g.mi <- coefse['g','Estimate']
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## est.g.se <- coefse['g','Std.Error']
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## result <- append(result,
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## list(Bgy.est.amelia.nok = est.g.mi,
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## Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
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## Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
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## ))
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## p <- v <- train <- rep(0,N)
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## M <- m
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## p[(M+1):(N)] <- 1
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## v[1:(M)] <- 1
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## df <- df[order(x.obs)]
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## y <- df[,y]
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## x <- df[,x.obs]
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## g <- df[,g]
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## w <- df[,w]
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## # gmm gets pretty close
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## (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=FALSE))
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## result <- append(result,
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## list(Bxy.est.gmm = gmm.res$beta[1,1],
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## Bxy.ci.upper.gmm = gmm.res$confint[1,2],
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## Bxy.ci.lower.gmm = gmm.res$confint[1,1]))
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## result <- append(result,
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## list(Bgy.est.gmm = gmm.res$beta[2,1],
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## Bgy.ci.upper.gmm = gmm.res$confint[2,2],
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## Bgy.ci.lower.gmm = gmm.res$confint[2,1]))
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## mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
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## (mod.calibrated.mle)
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## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
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## result <- append(result, list(
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## Bxy.est.mecor = mecor.ci['Estimate'],
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## Bxy.upper.mecor = mecor.ci['UCI'],
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## Bxy.lower.mecor = mecor.ci['LCI'])
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## )
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## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
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## result <- append(result, list(
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## Bxy.est.mecor = mecor.ci['Estimate'],
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## Bxy.upper.mecor = mecor.ci['UCI'],
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## Bxy.lower.mecor = mecor.ci['LCI'])
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## )
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## return(result)
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## }
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