Merge branch 'master' of code:ml_measurement_error_public

[ml_measurement_error_public.git] / simulations / simulation_base.R

diff --git a/simulations/simulation_base.R b/simulations/simulation_base.R
index a73ed79945c7e754ed0b122a385592839152b36d..27f0276f483999bcde37866972cf507c61233119 100644 (file)
--- a/simulations/simulation_base.R
+++ b/simulations/simulation_base.R
@@ -4,207 +4,398 @@ options(amelia.parallel="no",
         amelia.ncpus=1)
 library(Amelia)
 library(Zelig)
         amelia.ncpus=1)
 library(Amelia)
 library(Zelig)

-library(stats4)
+library(bbmle)
+library(matrixStats) # for numerically stable logsumexps

 
 

+source("measerr_methods.R") ## for my more generic function.

 
 ## 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 pseudolikelihood approach from Carroll page 349.
 ## assumes MAR
 ## assumes differential error, but that only depends on Y
 ## inefficient, because pseudolikelihood

-logistic.correction.pseudo <- function(df){
+    
+## 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)
     
     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, Bgy){
-        probs <- (1 - p0.est) + (p1.est + p0.est - 1)*plogis(B0 + Bxy * df$x + Bgy * df$g)
+    nll <- function(B0, Bxy, Bzy){

 
 

-        part1 = sum(log(probs[df$w_pred == 1]))
-        part2 = sum(log(1-probs[df$w_pred == 0]))
+        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)

         
         

-        return(-1*(part1 + part2))
+        probs <- colLogSumExps(rbind(log(1 - p0.est), log(p1.est + p0.est - 1) + pw))
+        return(-1*sum(probs))

     }
     
     }
     

-    mlefit <- stats4::mle(minuslogl = nll, start = list(B0=0, Bxy=0.0, Bgy=0.0))
+    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)
 
 }
 
     return(mlefit)
 
 }
 

+
+## model from Zhang's arxiv paper, with predictions for y
+## Zhang got this model from Hausman 1998
+### I think this is actually eqivalent to the pseudo.mle method
+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]
+    pn <- df.obs[(w_pred==0), .N]
+    npv <- tn / pn
+
+    tp <- df.obs[(w_pred==1) & (x.obs == w_pred),.N]
+    pp <- df.obs[(w_pred==1),.N]
+    ppv <- tp / pp
+
+    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)
+}
+
+## this is equivalent to the pseudo-liklihood model from Caroll
+## zhang.mle.dv <- function(df){
+
+##     nll <- function(B0=0, Bxy=0, Bzy=0, ppv=0.9, npv=0.9){
+##     df.obs <- df[!is.na(y.obs)]
+
+##     ## fpr = 1 - TNR
+##     ll.w0y0 <- with(df.obs[y.obs==0],dbinom(1-w_pred,1,npv,log=TRUE))
+##     ll.w1y1 <- with(df.obs[y.obs==1],dbinom(w_pred,1,ppv,log=TRUE))
+
+##     # 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) + sum(ll.w0y0) + sum(ll.w1y1)
+
+##     # unobserved case; integrate out y
+##     ## case y = 1
+##     ll.y.1 <- vector(mode='numeric', length=nrow(df))
+##     pi.y.1 <- with(df,plogis(B0 + Bxy * x + Bzy*z, log=T))
+##     ## P(w=1| y=1)P(y=1) + P(w=0|y=1)P(y=1) = P(w=1,y=1) + P(w=0,y=1)
+##     lls.y.1 <- colLogSumExps(rbind(log(ppv) + pi.y.1, log(1-ppv) + pi.y.1))
+    
+##     ## case y = 0
+##     ll.y.0 <- vector(mode='numeric', length=nrow(df))
+##     pi.y.0 <- with(df,plogis(B0 + Bxy * x + Bzy*z, log=T,lower.tail=FALSE))
+
+##     ## P(w=1 | y=0)P(y=0) + P(w=0|y=0)P(y=0) = P(w=1,y=0) + P(w=0,y=0)
+##     lls.y.0 <- colLogSumExps(rbind(log(npv) + pi.y.0, log(1-npv) + pi.y.0))
+
+##     lls <- colLogSumExps(rbind(lls.y.1, lls.y.0))
+##     ll <- ll + sum(lls)
+##     return(-ll)
+##     }    
+##     mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6),method='L-BFGS-B',lower=list(B0=-Inf, Bxy=-Inf, Bzy=-Inf, ppv=0.001,npv=0.001),
+##                    upper=list(B0=Inf, Bxy=Inf, Bzy=Inf,ppv=0.999,npv=0.999))
+##     return(mlefit)
+## }
+
+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]
+    p <- df.obs[(w_pred==1),.N]
+    fpr <- fp / p
+    fn <- df.obs[(w_pred==0) & (y.obs != w_pred), .N]
+    n <- df.obs[(w_pred==0),.N]
+    fnr <- fn / n
+
+    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,plogis(B0 + Bxy * x + Bzy*z, log=T))
+        pi.y.0 <- with(df,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) * colLogSumExps(rbind(log(1-fpr), log(1 - fnr - fpr)+pi.y.0)))))
+    
+        ll <- ll + sum(lls)
+        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)
+}
+ 

 ## This uses the likelihood approach from Carroll page 353.
 ## assumes that we have a good measurement error model
 ## This uses the likelihood approach from Carroll page 353.
 ## assumes that we have a good measurement error model

-logistic.correction.liklihood <- function(df){
+my.mle <- function(df){

     
     ## liklihood for observed responses
     
     ## liklihood for observed responses

-    nll <- function(B0, Bxy, Bgy, gamma0, gamma_y, gamma_g){
+    nll <- function(B0, Bxy, Bzy, gamma0, gamma_y, gamma_z, gamma_yz){

         df.obs <- df[!is.na(y.obs)]
         df.obs <- df[!is.na(y.obs)]

-        p.y.obs <- plogis(B0 + Bxy * df.obs$x + Bgy*df.obs$g)
-        p.y.obs[df.obs$y==0] <- 1-p.y.obs[df.obs$y==0]
-        p.s.obs <- plogis(gamma0 + gamma_y * df.obs$y + gamma_g*df.obs$g)
-        p.s.obs[df.obs$w_pred==0] <- 1 - p.s.obs[df.obs$w_pred==0]
+        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.s.obs * p.y.obs
+        p.obs <- p.w.obs + p.y.obs

 
         df.unobs <- df[is.na(y.obs)]
 
 
         df.unobs <- df[is.na(y.obs)]
 

-        p.unobs.1 <- plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g)*plogis(gamma0 + gamma_y + gamma_g*df.unobs$g)
-        p.unobs.0 <- (1-plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g))*plogis(gamma0 + gamma_g*df.unobs$g)
-        p.unobs <- p.unobs.1 + p.unobs.0
-        p.unobs[df.unobs$w_pred==0] <- 1 - p.unobs[df.unobs$w_pred==0]
+        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)
 
 
         p <- c(p.obs, p.unobs)
 

-        return(-1*(sum(log(p))))
+        return(-1*(sum(p)))

     }
 
     }
 

-    mlefit <- stats4::mle(minuslogl = nll, start = list(B0=1, Bxy=0,Bgy=0, gamma0=5, gamma_y=0, gamma_g=0))
+    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)
 }
 
 
     return(mlefit)
 }
 

-
-logistic <- function(x) {1/(1+exp(-1*x))}
-
-run_simulation_depvar <- function(df, result){
+run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y){

 
     accuracy <- df[,mean(w_pred==y)]
     result <- append(result, list(accuracy=accuracy))
 
     accuracy <- df[,mean(w_pred==y)]
     result <- append(result, list(accuracy=accuracy))

+    error.cor.x <- cor(df$x, df$w - df$x)
+    result <- append(result, list(error.cor.x = error.cor.x))
+
+    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 <- glm(y ~ x + g, data=df,family=binomial(link='logit')))

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

 
     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]))
 
 
     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]))
 

-    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 <- glm(w_pred~x+g, data=df, family=binomial(link='logit')))
+    (model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))

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

-    naive.ci.Bgy <- confint(model.naive)['g',]
+    naive.ci.Bzy <- confint(model.naive)['z',]

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

-                                  Bgy.est.naive=coef(model.naive)['g'],
+                                  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+g, data=df))
+    (model.naive.cont <- lm(w~x+z, data=df))

     naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
     naivecont.ci.Bxy <- confint(model.naive.cont)['x',]

-    naivecont.ci.Bgy <- confint(model.naive.cont)['g',]
+    naivecont.ci.Bzy <- confint(model.naive.cont)['z',]

 
 

-    ## my implementatoin of liklihood based correction
-    mod.caroll.lik <- logistic.correction.liklihood(df)
-    coef <- coef(mod.caroll.lik)
-    ci <- confint(mod.caroll.lik)
+    ## my implementation of liklihood based correction

 
 

+    temp.df <- copy(df)
+    temp.df[,y:=y.obs]
+    mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+    fisher.info <- solve(mod.caroll.lik$hessian)
+    coef <- mod.caroll.lik$par
+    ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
+    ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96

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

-                     list(Bxy.est.mle = coef['Bxy'],
-                          Bxy.ci.upper.mle = ci['Bxy','97.5 %'],
-                          Bxy.ci.lower.mle = ci['Bxy','2.5 %'],
-                          Bgy.est.mle = coef['Bgy'],
-                          Bgy.ci.upper.mle = ci['Bgy','97.5 %'],
-                          Bgy.ci.lower.mle = ci['Bgy','2.5 %']))
-                          
+                     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']))
+

 
     ## my implementatoin of liklihood based correction
 
     ## my implementatoin of liklihood based correction

-    mod.caroll.pseudo <- logistic.correction.pseudo(df)
-    coef <- coef(mod.caroll.pseudo)
-    ci <- confint(mod.caroll.pseudo)
+    mod.zhang <- zhang.mle.dv(df)
+    coef <- coef(mod.zhang)
+    ci <- confint(mod.zhang,method='quad')

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

-                     list(Bxy.est.pseudo = coef['Bxy'],
-                          Bxy.ci.upper.pseudo = ci['Bxy','97.5 %'],
-                          Bxy.ci.lower.pseudo = ci['Bxy','2.5 %'],
-                          Bgy.est.pseudo = coef['Bgy'],
-                          Bgy.ci.upper.pseudo = ci['Bgy','97.5 %'],
-                          Bgy.ci.lower.pseudo = ci['Bgy','2.5 %']))
-                          
+                     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.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w_pred'))
-    mod.amelia.k <- zelig(y.obs~x+g, 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']
-    result <- append(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
-                          ))
+    

 
 

-    est.g.mi <- coefse['g','Estimate']
-    est.g.se <- coefse['g','Std.Error']
+    # amelia says use normal distribution for binary variables.
+    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$imputations, cite=FALSE)
+        (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+        est.x.mi <- coefse['x','Estimate']
+        est.x.se <- coefse['x','Std.Error']
+        result <- append(result,
+                         list(Bxy.est.amelia.full = est.x.mi,
+                              Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
+                              Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
+                              ))
+
+        est.z.mi <- coefse['z','Estimate']
+        est.z.se <- coefse['z','Std.Error']
+
+        result <- append(result,
+                         list(Bzy.est.amelia.full = est.z.mi,
+                              Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
+                              Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
+                              ))
+
+    },
+    error = function(e){
+        message("An error occurred:\n",e)
+        result$error <- paste0(result$error,'\n', e)
+    })

 
 

-    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
-                          ))

 
     return(result)
 
 }
 
 
     return(result)
 
 }
 

-run_simulation <-  function(df, result){

 
 

-    accuracy <- df[,mean(w_pred==x)]
-    result <- append(result, list(accuracy=accuracy))
+## 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){

 
 

-    (model.true <- lm(y ~ x + g, data=df))
+    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.Bxy <- confint(model.true)['x',]

-    true.ci.Bgy <- confint(model.true)['g',]
+    true.ci.Bzy <- confint(model.true)['z',]

 
     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 <- 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.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.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))
+    (model.naive <- lm(y~w_pred+z, data=df))

     
     

-    naive.ci.Bxy <- confint(model.naive)['w',]
-    naive.ci.Bgy <- confint(model.naive)['g',]
+    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'],
-                                  Bgy.est.naive=coef(model.naive)['g'],
+    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],
                                   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]))

                                   
 
                                   
 

-    amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
-    mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+    tryCatch({
+    amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
+    mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)

     (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
 
     est.x.mi <- coefse['x.obs','Estimate']
     (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
 
     est.x.mi <- coefse['x.obs','Estimate']


@@ -215,15 +406,65 @@ run_simulation <-  function(df, result){
                           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
                           ))
 

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

 
     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(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){
+        message("An error occurred:\n",e)
+        result$error <-paste0(result$error,'\n', e)
+    }
+    )
+
+    tryCatch({
+        temp.df <- copy(df)
+        temp.df <- temp.df[,x:=x.obs]
+        mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
+        fisher.info <- solve(mod.caroll.lik$hessian)
+        coef <- mod.caroll.lik$par
+        ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
+        ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
+        
+        
+        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']))
+    },
+
+    error = function(e){
+        message("An error occurred:\n",e)
+        result$error <- paste0(result$error,'\n', e)
+    })
+
+    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 %']))
+    },
+
+    error = function(e){
+        message("An error occurred:\n",e)
+        result$error <- paste0(result$error,'\n', e)
+    })
+

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


@@ -255,10 +496,10 @@ 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],


@@ -268,28 +509,34 @@ 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')
+    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'],
     (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'])
+                                 Bxy.ci.upper.mecor = mecor.ci['UCI'],
+                                 Bxy.ci.lower.mecor = mecor.ci['LCI'])

                      )
 
                      )
 

-    (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
+    (mecor.ci <- summary(mod.calibrated.mle)$c$ci['z',])

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

-                                 Bgy.est.mecor = mecor.ci['Estimate'],
-                                 Bgy.upper.mecor = mecor.ci['UCI'],
-                                 Bgy.lower.mecor = mecor.ci['LCI'])
+                                 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
 ##    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"))
     
 ##    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"))