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
-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)
- 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)
}
+
+## 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
-logistic.correction.liklihood <- function(df){
+my.mle <- function(df){
## 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)]
- 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.obs <- p.s.obs * p.y.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.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)
- 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)
}
-
-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))
- (model.true <- glm(y ~ x + g, data=df,family=binomial(link='logit')))
+ (model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
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'],
- 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],
- 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.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.Bgy <- confint(model.naive)['g',]
+ naive.ci.Bzy <- confint(model.naive)['z',]
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],
- 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.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,
- 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
- 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,
- 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 %']))
-
-
- # 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$imputations, cite=FALSE)
- (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+ list(Bxy.est.zhang = coef['Bxy'],
+ Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
+ Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
+ Bzy.est.zhang = coef['Bzy'],
+ Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
+ Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
- est.x.mi <- coefse['x','Estimate']
- est.x.se <- coefse['x','Std.Error']
- result <- append(result,
- list(Bxy.est.amelia.full = est.x.mi,
- Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
- Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
- ))
+
- est.g.mi <- coefse['g','Estimate']
- est.g.se <- coefse['g','Std.Error']
+ # amelia says use normal distribution for binary variables.
+ tryCatch({
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
+ mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$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)
}
-run_simulation <- function(df, 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){
accuracy <- df[,mean(w_pred==x)]
result <- append(result, list(accuracy=accuracy))
- (model.true <- lm(y ~ x + g, data=df))
+ (model.true <- lm(y ~ x + z, data=df))
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'],
- 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],
- 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.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],
- 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']
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,
- 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$imputations, cite=FALSE)
df <- df[order(x.obs)]
y <- df[,y]
x <- df[,x.obs]
- g <- df[,g]
- w <- df[,w]
+ z <- df[,z]
+ w <- df[,w_pred]
# gmm gets pretty close
- (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=TRUE))
+ (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))
result <- append(result,
list(Bxy.est.gmm = gmm.res$beta[1,1],
))
result <- append(result,
- list(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'],
- 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(
- 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"))
projects / ml_measurement_error_public.git / blobdiff