amelia.ncpus=1)
library(Amelia)
library(Zelig)
+library(stats4)
+
+
+## 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){
+ 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)
+
+ part1 = sum(log(probs[df$w_pred == 1]))
+ part2 = sum(log(1-probs[df$w_pred == 0]))
+
+ return(-1*(part1 + part2))
+ }
+
+ mlefit <- stats4::mle(minuslogl = nll, start = list(B0=0, Bxy=0.0, Bgy=0.0))
+ 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){
+
+ ## liklihood for observed responses
+ nll <- function(B0, Bxy, Bgy, gamma0, gamma_y, gamma_g){
+ 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]
+
+ p.obs <- p.s.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 <- c(p.obs, p.unobs)
+
+ return(-1*(sum(log(p))))
+ }
+
+ mlefit <- stats4::mle(minuslogl = nll, start = list(B0=1, Bxy=0,Bgy=0, gamma0=5, gamma_y=0, gamma_g=0))
+
+ return(mlefit)
+}
+
logistic <- function(x) {1/(1+exp(-1*x))}
+run_simulation_depvar <- function(df, result){
+
+ accuracy <- df[,mean(w_pred==y)]
+ result <- append(result, list(accuracy=accuracy))
+
+ (model.true <- glm(y ~ x + g, data=df,family=binomial(link='logit')))
+ true.ci.Bxy <- confint(model.true)['x',]
+ true.ci.Bgy <- confint(model.true)['g',]
+
+ result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
+ Bgy.est.true=coef(model.true)['g'],
+ 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]))
+
+ (model.feasible <- glm(y.obs~x+g,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]))
+
+ (model.naive <- glm(w_pred~x+g, data=df, family=binomial(link='logit')))
+
+ naive.ci.Bxy <- confint(model.naive)['x',]
+ naive.ci.Bgy <- confint(model.naive)['g',]
+
+ result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
+ Bgy.est.naive=coef(model.naive)['g'],
+ 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]))
+
+
+ (model.naive.cont <- lm(w~x+g, data=df))
+ naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
+ naivecont.ci.Bgy <- confint(model.naive.cont)['g',]
+
+ ## my implementatoin of liklihood based correction
+ mod.caroll.lik <- logistic.correction.liklihood(df)
+ coef <- coef(mod.caroll.lik)
+ ci <- confint(mod.caroll.lik)
+
+ 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 %']))
+
+
+ ## my implementatoin of liklihood based correction
+ mod.caroll.pseudo <- logistic.correction.pseudo(df)
+ coef <- coef(mod.caroll.pseudo)
+ ci <- confint(mod.caroll.pseudo)
+
+ 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$imputations, cite=FALSE)
+ (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+
+ est.x.mi <- coefse['x','Estimate']
+ est.x.se <- coefse['x','Std.Error']
+ result <- append(result,
+ list(Bxy.est.amelia.full = est.x.mi,
+ Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
+ Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
+ ))
+
+ est.g.mi <- coefse['g','Estimate']
+ est.g.se <- coefse['g','Std.Error']
+
+ result <- append(result,
+ list(Bgy.est.amelia.full = est.g.mi,
+ Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
+ Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
+ ))
+
+ return(result)
+
+}
+
run_simulation <- function(df, result){
accuracy <- df[,mean(w_pred==x)]
Bgy.ci.lower.naive = naive.ci.Bgy[1]))
- ## multiple imputation when k is observed
- ## amelia does great at this one.
- noms <- c()
- if(length(unique(df$x.obs)) <=2){
- noms <- c(noms, 'x.obs')
- }
-
- if(length(unique(df$g)) <=2){
- noms <- c(noms, 'g')
- }
-
-
- amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=noms)
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
projects / ml_measurement_error_public.git / blobdiff