real-data example on raw perspective scores

[ml_measurement_error_public.git] / simulations / simulation_base.R

diff --git a/simulations/simulation_base.R b/simulations/simulation_base.R
index 26916abb7dee3f0a509648cb2ef3ba6ecc64cffd..bafd7d34bba08ccd43513e3d699f4e3090e8fa30 100644 (file)
--- a/simulations/simulation_base.R
+++ b/simulations/simulation_base.R
@@ -4,104 +4,402 @@ options(amelia.parallel="no",
         amelia.ncpus=1)
 library(Amelia)
 library(Zelig)
         amelia.ncpus=1)
 library(Amelia)
 library(Zelig)

+library(bbmle)
+library(matrixStats) # for numerically stable logsumexps

 
 

-logistic <- function(x) {1/(1+exp(-1*x))}
+source("pl_methods.R")
+source("measerr_methods.R") ## for my more generic function.

 
 

-run_simulation <-  function(df, result){
+## This uses the pseudolikelihood approach from Carroll page 349.
+## assumes MAR
+## assumes differential error, but that only depends on Y
+## inefficient, because pseudolikelihood
+    
+## This uses the pseudo-likelihood approach from Carroll page 346.
+my.pseudo.mle <- function(df){
+    p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
+    p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
+    
+    nll <- function(B0, Bxy, Bzy){

 
 

-    accuracy <- df[,mean(w_pred==x)]
+        pw <- vector(mode='numeric',length=nrow(df))
+        dfw1 <- df[w_pred==1]
+        dfw0 <- df[w_pred==0]
+        pw[df$w_pred==1] <- plogis(B0 + Bxy * dfw1$x + Bzy * dfw1$z, log=T)
+        pw[df$w_pred==0] <- plogis(B0 + Bxy * dfw0$x + Bzy * dfw0$z, lower.tail=FALSE, log=T)
+        
+        probs <- colLogSumExps(rbind(log(1 - p0.est), log(p1.est + p0.est - 1) + pw))
+        return(-1*sum(probs))
+    }
+    
+    mlefit <- mle2(minuslogl = nll, start = list(B0=0.0, Bxy=0.0, Bzy=0.0), control=list(maxit=1e6),method='L-BFGS-B')
+    return(mlefit)
+
+}
+
+ 
+## This uses the likelihood approach from Carroll page 353.
+## assumes that we have a good measurement error model
+my.mle <- function(df){
+    
+    ## liklihood for observed responses
+    nll <- function(B0, Bxy, Bzy, gamma0, gamma_y, gamma_z, gamma_yz){
+        df.obs <- df[!is.na(y.obs)]
+        yobs0 <- df.obs$y==0 
+        yobs1 <- df.obs$y==1
+        p.y.obs <- vector(mode='numeric', length=nrow(df.obs))
+        
+        p.y.obs[yobs1] <- plogis(B0 + Bxy * df.obs[yobs1]$x + Bzy*df.obs[yobs1]$z,log=T)
+        p.y.obs[yobs0] <- plogis(B0 + Bxy * df.obs[yobs0]$x + Bzy*df.obs[yobs0]$z,lower.tail=FALSE,log=T)
+
+        wobs0 <- df.obs$w_pred==0
+        wobs1 <- df.obs$w_pred==1
+        p.w.obs <- vector(mode='numeric', length=nrow(df.obs))
+
+        p.w.obs[wobs1] <- plogis(gamma0 + gamma_y * df.obs[wobs1]$y + gamma_z*df.obs[wobs1]$z + df.obs[wobs1]$z*df.obs[wobs1]$y* gamma_yz, log=T)
+        p.w.obs[wobs0] <- plogis(gamma0 + gamma_y * df.obs[wobs0]$y + gamma_z*df.obs[wobs0]$z + df.obs[wobs0]$z*df.obs[wobs0]$y* gamma_yz, lower.tail=FALSE, log=T)
+        
+        p.obs <- p.w.obs + p.y.obs
+
+        df.unobs <- df[is.na(y.obs)]
+
+        p.unobs.0 <- vector(mode='numeric',length=nrow(df.unobs))
+        p.unobs.1 <- vector(mode='numeric',length=nrow(df.unobs))
+
+        wunobs.0 <- df.unobs$w_pred == 0
+        wunobs.1 <- df.unobs$w_pred == 1
+        
+        p.unobs.0[wunobs.1] <- plogis(B0 + Bxy * df.unobs[wunobs.1]$x + Bzy*df.unobs[wunobs.1]$z, log=T) + plogis(gamma0 + gamma_y + gamma_z*df.unobs[wunobs.1]$z + df.unobs[wunobs.1]$z*gamma_yz, log=T)
+
+        p.unobs.0[wunobs.0] <- plogis(B0 + Bxy * df.unobs[wunobs.0]$x + Bzy*df.unobs[wunobs.0]$z, log=T) + plogis(gamma0 + gamma_y + gamma_z*df.unobs[wunobs.0]$z + df.unobs[wunobs.0]$z*gamma_yz, lower.tail=FALSE, log=T)
+
+        p.unobs.1[wunobs.1] <- plogis(B0 + Bxy * df.unobs[wunobs.1]$x + Bzy*df.unobs[wunobs.1]$z, log=T, lower.tail=FALSE) + plogis(gamma0 + gamma_z*df.unobs[wunobs.1]$z, log=T)
+
+        p.unobs.1[wunobs.0] <- plogis(B0 + Bxy * df.unobs[wunobs.0]$x + Bzy*df.unobs[wunobs.0]$z, log=T, lower.tail=FALSE) + plogis(gamma0 + gamma_z*df.unobs[wunobs.0]$z, lower.tail=FALSE, log=T)
+
+        p.unobs <- colLogSumExps(rbind(p.unobs.1, p.unobs.0))
+
+        p <- c(p.obs, p.unobs)
+
+        return(-1*(sum(p)))
+    }
+
+    mlefit <- mle2(minuslogl = nll, start = list(B0=0, Bxy=0,Bzy=0, gamma0=0, gamma_y=0, gamma_z=0, gamma_yz=0), control=list(maxit=1e6),method='L-BFGS-B')
+
+    return(mlefit)
+}
+
+run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y, confint_method='quad'){
+
+    (accuracy <- df[,mean(w_pred==y)])

     result <- append(result, list(accuracy=accuracy))
     result <- append(result, list(accuracy=accuracy))

+    (error.cor.z <- cor(df$z, df$y - df$w_pred))
+    (error.cor.x <- cor(df$x, df$y - df$w_pred))
+    (error.cor.y <- cor(df$y, df$y - df$w_pred))
+    result <- append(result, list(error.cor.x = error.cor.x,
+                                  error.cor.z = error.cor.z,
+                                  error.cor.y = error.cor.y))
+
+    model.null <- glm(y~1, data=df,family=binomial(link='logit'))
+    (model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
+    (lik.ratio <- exp(logLik(model.true) - logLik(model.null)))

 
 

-    (model.true <- lm(y ~ x + g, data=df))

     true.ci.Bxy <- confint(model.true)['x',]
     true.ci.Bxy <- confint(model.true)['x',]

-    true.ci.Bgy <- confint(model.true)['g',]
+    true.ci.Bzy <- confint(model.true)['z',]
+
+    result <- append(result, list(cor.xz=cor(df$x,df$z)))
+    result <- append(result, list(lik.ratio=lik.ratio))

 
     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
 
     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],

-                                  Bgy.est.true=coef(model.true)['g'],
+                                  Bzy.est.true=coef(model.true)['z'],

                                   Bxy.ci.upper.true = true.ci.Bxy[2],
                                   Bxy.ci.lower.true = true.ci.Bxy[1],
                                   Bxy.ci.upper.true = true.ci.Bxy[2],
                                   Bxy.ci.lower.true = true.ci.Bxy[1],

-                                  Bgy.ci.upper.true = true.ci.Bgy[2],
-                                  Bgy.ci.lower.true = true.ci.Bgy[1]))
+                                  Bzy.ci.upper.true = true.ci.Bzy[2],
+                                  Bzy.ci.lower.true = true.ci.Bzy[1]))

                                   
                                   

-    (model.feasible <- lm(y~x.obs+g,data=df))
+    (model.feasible <- glm(y.obs~x+z,data=df,family=binomial(link='logit')))

 
 

-    feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
-    result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
+    feasible.ci.Bxy <- confint(model.feasible)['x',]
+    result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],

                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
 
                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
 

-    feasible.ci.Bgy <- confint(model.feasible)['g',]
-    result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
-                                  Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
-                                  Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
+    feasible.ci.Bzy <- confint(model.feasible)['z',]
+    result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
+                                  Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
+                                  Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))

 
 

-    (model.naive <- lm(y~w+g, data=df))
-    
-    naive.ci.Bxy <- confint(model.naive)['w',]
-    naive.ci.Bgy <- confint(model.naive)['g',]
+    (model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))
+
+    naive.ci.Bxy <- confint(model.naive)['x',]
+    naive.ci.Bzy <- confint(model.naive)['z',]

 
 

-    result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
-                                  Bgy.est.naive=coef(model.naive)['g'],
+    result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
+                                  Bzy.est.naive=coef(model.naive)['z'],

                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],

-                                  Bgy.ci.upper.naive = naive.ci.Bgy[2],
-                                  Bgy.ci.lower.naive = naive.ci.Bgy[1]))
-                                  
+                                  Bzy.ci.upper.naive = naive.ci.Bzy[2],
+                                  Bzy.ci.lower.naive = naive.ci.Bzy[1]))
+
+
+    (model.naive.cont <- lm(w~x+z, data=df))
+    naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
+    naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
+
+    ## my implementation of liklihood based correction

 
 

-    ## multiple imputation when k is observed
-    ## amelia does great at this one.
-    noms <- c()
-    if(length(unique(df$x.obs)) <=2){
-        noms <- c(noms, 'x.obs')
+    temp.df <- copy(df)
+    temp.df[,y:=y.obs]
+
+    if(confint_method=='quad'){
+        mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+        fischer.info <- solve(mod.caroll.lik$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'

 
 

-    if(length(unique(df$g)) <=2){
-        noms <- c(noms, 'g')
+        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 %']

     }
 
     }
 

+    result <- append(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']))
+

 
 

-    amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=noms)
-    mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
-    (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+    ## my implementatoin of liklihood based correction
+    mod.zhang <- zhang.mle.dv(df)
+    coef <- coef(mod.zhang)
+    ci <- confint(mod.zhang,method='quad')

 
 

-    est.x.mi <- coefse['x.obs','Estimate']
-    est.x.se <- coefse['x.obs','Std.Error']

     result <- append(result,
     result <- append(result,

-                     list(Bxy.est.amelia.full = est.x.mi,
+                     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 %']))
+
+    
+
+    # amelia says use normal distribution for binary variables.
+    amelia_result <- list(Bxy.est.amelia.full = NA,
+                          Bxy.ci.upper.amelia.full = NA,
+                          Bxy.ci.lower.amelia.full = NA,
+                          Bzy.est.amelia.full = NA,
+                          Bzy.ci.upper.amelia.full = NA,
+                          Bzy.ci.lower.amelia.full = NA
+                          )
+
+    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)
+        (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+        est.x.mi <- coefse['x','Estimate']
+        est.x.se <- coefse['x','Std.Error']
+
+        est.z.mi <- coefse['z','Estimate']
+        est.z.se <- coefse['z','Std.Error']
+        amelia_result <- list(Bxy.est.amelia.full = est.x.mi,

                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,

-                          Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
-                          ))
+                          Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
+                          Bzy.est.amelia.full = est.z.mi,
+                          Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
+                          Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
+                          )
+    },
+    error = function(e){
+    result[['error']] <- e}
+    )
+    result <- append(result,amelia_result)

 
 

-    est.g.mi <- coefse['g','Estimate']
-    est.g.se <- coefse['g','Std.Error']
+    return(result)

 
 

+}
+
+
+## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle 
+run_simulation <-  function(df, result, outcome_formula=y~x+z, proxy_formula=NULL, truth_formula=NULL, confint_method='quad'){
+
+    accuracy <- df[,mean(w_pred==x)]
+    accuracy.y0 <- df[y<=0,mean(w_pred==x)]
+    accuracy.y1 <- df[y>=0,mean(w_pred==x)]
+    cor.y.xi <- cor(df$x - df$w_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.y0=accuracy.y0,
+                                  accuracy.y1=accuracy.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]))
+                                  
+    (model.feasible <- lm(y~x.obs+z,data=df))
+
+    feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
+    result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
+                                  Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
+                                  Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
+
+    feasible.ci.Bzy <- confint(model.feasible)['z',]
+    result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
+                                  Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
+                                  Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
+
+    (model.naive <- lm(y~w_pred+z, data=df))
+    
+    naive.ci.Bxy <- confint(model.naive)['w_pred',]
+    naive.ci.Bzy <- confint(model.naive)['z',]
+
+    result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'],
+                                  Bzy.est.naive=coef(model.naive)['z'],
+                                  Bxy.ci.upper.naive = naive.ci.Bxy[2],
+                                  Bxy.ci.lower.naive = naive.ci.Bxy[1],
+                                  Bzy.ci.upper.naive = naive.ci.Bzy[2],
+                                  Bzy.ci.lower.naive = naive.ci.Bzy[1]))
+
+    amelia_result <- list(
+        Bxy.est.amelia.full = NULL,
+        Bxy.ci.upper.amelia.full = NULL,
+        Bxy.ci.lower.amelia.full = NULL,
+        Bzy.est.amelia.full = NULL,
+        Bzy.ci.upper.amelia.full = NULL,
+        Bzy.ci.lower.amelia.full = NULL
+        )
+
+    tryCatch({
+        amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
+        mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+        (coefse <- combine_coef_se(mod.amelia.k))
+
+        est.x.mi <- coefse['x.obs','Estimate']
+        est.x.se <- coefse['x.obs','Std.Error']
+        est.z.mi <- coefse['z','Estimate']
+        est.z.se <- coefse['z','Std.Error']
+
+        amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
+                              Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
+                              Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
+                              Bzy.est.amelia.full = est.z.mi,
+                              Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
+                              Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
+                              )
+
+    },
+
+    error = function(e){
+        result[['error']] <- e}
+    )
+
+
+    result <- append(result, amelia_result)
+
+
+   mle_result <- list(Bxy.est.mle = NULL,
+                      Bxy.ci.upper.mle = NULL,
+                      Bxy.ci.lower.mle = NULL,
+                      Bzy.est.mle = NULL,
+                      Bzy.ci.upper.mle = NULL,
+                      Bzy.ci.lower.mle = NULL)
+
+    tryCatch({
+        temp.df <- copy(df)
+        temp.df <- temp.df[,x:=x.obs]
+        if(confint_method=='quad'){
+            mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='optim')
+            fischer.info <- solve(mod.caroll.lik$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='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)
+
+    mod.zhang.lik <- zhang.mle.iv(df)
+    coef <- coef(mod.zhang.lik)
+    ci <- confint(mod.zhang.lik,method='quad')

     result <- append(result,
     result <- append(result,

-                     list(Bgy.est.amelia.full = est.g.mi,
-                          Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
-                          Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
-                          ))
+                     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 %']))

 
     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
 
     ## 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","k","w_pred"), noms=noms)
-    mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
-    (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
+    ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
+    ## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
+    ## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))

 
 

-    est.x.mi <- coefse['x.obs','Estimate']
-    est.x.se <- coefse['x.obs','Std.Error']
-    result <- append(result,
-                     list(Bxy.est.amelia.nok = est.x.mi,
-                          Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
-                          Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
-                          ))
+    ## est.x.mi <- coefse['x.obs','Estimate']
+    ## est.x.se <- coefse['x.obs','Std.Error']
+    ## result <- append(result,
+    ##                  list(Bxy.est.amelia.nok = est.x.mi,
+    ##                       Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
+    ##                       Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
+    ##                       ))

 
 

-    est.g.mi <- coefse['g','Estimate']
-    est.g.se <- coefse['g','Std.Error']
+    ## est.g.mi <- coefse['g','Estimate']
+    ## est.g.se <- coefse['g','Std.Error']

 
 

-    result <- append(result,
-                     list(Bgy.est.amelia.nok = est.g.mi,
-                          Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
-                          Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
-                          ))
+    ## result <- append(result,
+    ##                  list(Bgy.est.amelia.nok = est.g.mi,
+    ##                       Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
+    ##                       Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
+    ##                       ))

 
     N <- nrow(df)
     m <- nrow(df[!is.na(x.obs)])
 
     N <- nrow(df)
     m <- nrow(df[!is.na(x.obs)])


@@ -112,10 +410,10 @@ run_simulation <-  function(df, result){
     df <- df[order(x.obs)]
     y <- df[,y]
     x <- df[,x.obs]
     df <- df[order(x.obs)]
     y <- df[,y]
     x <- df[,x.obs]

-    g <- df[,g]
-    w <- df[,w]
+    z <- df[,z]
+    w <- df[,w_pred]

     # gmm gets pretty close
     # gmm gets pretty close

-    (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=TRUE))
+    (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))

 
     result <- append(result,
                      list(Bxy.est.gmm = gmm.res$beta[1,1],
 
     result <- append(result,
                      list(Bxy.est.gmm = gmm.res$beta[1,1],


@@ -125,31 +423,37 @@ run_simulation <-  function(df, result){
                           ))
 
     result <- append(result,
                           ))
 
     result <- append(result,

-                     list(Bgy.est.gmm = gmm.res$beta[2,1],
-                          Bgy.ci.upper.gmm = gmm.res$confint[2,2],
-                          Bgy.ci.lower.gmm = gmm.res$confint[2,1]))
-
+                     list(Bzy.est.gmm = gmm.res$beta[2,1],
+                          Bzy.ci.upper.gmm = gmm.res$confint[2,2],
+                          Bzy.ci.lower.gmm = gmm.res$confint[2,1]))

 
 

-    mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
-    (mod.calibrated.mle)
-    (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
-    result <- append(result, list(
-                                 Bxy.est.mecor = mecor.ci['Estimate'],
-                                 Bxy.upper.mecor = mecor.ci['UCI'],
-                                 Bxy.lower.mecor = mecor.ci['LCI'])
-                     )

 
 

-    (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
+    ## tryCatch({
+    ## mod.calibrated.mle <- mecor(y ~ MeasError(w_pred, reference = x.obs) + z, df, B=400, method='efficient')
+    ## (mod.calibrated.mle)
+    ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
+    ## result <- append(result, list(
+    ##                              Bxy.est.mecor = mecor.ci['Estimate'],
+    ##                              Bxy.ci.upper.mecor = mecor.ci['UCI'],
+    ##                              Bxy.ci.lower.mecor = mecor.ci['LCI'])
+    ##                  )

 
 

-    result <- append(result, list(
-                                 Bgy.est.mecor = mecor.ci['Estimate'],
-                                 Bgy.upper.mecor = mecor.ci['UCI'],
-                                 Bgy.lower.mecor = mecor.ci['LCI'])
-                     )
+    ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['z',])

 
 

+    ## result <- append(result, list(
+    ##                              Bzy.est.mecor = mecor.ci['Estimate'],
+    ##                              Bzy.ci.upper.mecor = mecor.ci['UCI'],
+    ##                              Bzy.ci.lower.mecor = mecor.ci['LCI'])
+    ##                  )
+    ## },
+    ## error = function(e){
+    ##     message("An error occurred:\n",e)
+    ##     result$error <- paste0(result$error, '\n', e)
+    ## }
+    ## )

 ##    clean up memory
 ##    clean up memory

-    rm(list=c("df","y","x","g","w","v","train","p","amelia.out.k","amelia.out.nok", "mod.calibrated.mle","gmm.res","mod.amelia.k","mod.amelia.nok", "model.true","model.naive","model.feasible"))
+##    rm(list=c("df","y","x","g","w","v","train","p","amelia.out.k","amelia.out.nok", "mod.calibrated.mle","gmm.res","mod.amelia.k","mod.amelia.nok", "model.true","model.naive","model.feasible"))

     
     

-    gc()
+##    gc()

     return(result)
 }
     return(result)
 }