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){
+
+ (accuracy <- df[,mean(w_pred==y)])
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$w_pred))
+ result <- append(result, list(error.cor.x = error.cor.x,
+ error.cor.z = error.cor.z,
+ error.cor.y = error.cor.y))
+
+ model.null <- glm(y~1, data=df,family=binomial(link='logit'))
+ (model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
+ (lik.ratio <- exp(logLik(model.true) - logLik(model.null)))
- (model.true <- lm(y ~ x + g, data=df))
true.ci.Bxy <- confint(model.true)['x',]
- true.ci.Bgy <- confint(model.true)['g',]
+ true.ci.Bzy <- confint(model.true)['z',]
+
+ result <- append(result, list(cor.xz=cor(df$x,df$z)))
+ result <- append(result, list(lik.ratio=lik.ratio))
result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
- Bgy.est.true=coef(model.true)['g'],
+ Bzy.est.true=coef(model.true)['z'],
Bxy.ci.upper.true = true.ci.Bxy[2],
Bxy.ci.lower.true = true.ci.Bxy[1],
- Bgy.ci.upper.true = true.ci.Bgy[2],
- Bgy.ci.lower.true = true.ci.Bgy[1]))
+ Bzy.ci.upper.true = true.ci.Bzy[2],
+ Bzy.ci.lower.true = true.ci.Bzy[1]))
- (model.feasible <- lm(y~x.obs+g,data=df))
+ (model.feasible <- glm(y.obs~x+z,data=df,family=binomial(link='logit')))
+
+ feasible.ci.Bxy <- confint(model.feasible)['x',]
+ result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
+ Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
+ Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
+
+ feasible.ci.Bzy <- confint(model.feasible)['z',]
+ result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
+ Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
+ Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
+
+ (model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))
+
+ naive.ci.Bxy <- confint(model.naive)['x',]
+ naive.ci.Bzy <- confint(model.naive)['z',]
+
+ result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
+ Bzy.est.naive=coef(model.naive)['z'],
+ Bxy.ci.upper.naive = naive.ci.Bxy[2],
+ Bxy.ci.lower.naive = naive.ci.Bxy[1],
+ Bzy.ci.upper.naive = naive.ci.Bzy[2],
+ Bzy.ci.lower.naive = naive.ci.Bzy[1]))
+
+
+ (model.naive.cont <- lm(w~x+z, data=df))
+ naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
+ naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
+
+ ## my implementation of liklihood based correction
+
+ temp.df <- copy(df)
+ temp.df[,y:=y.obs]
+ mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+ fischer.info <- solve(mod.caroll.lik$hessian)
+ coef <- mod.caroll.lik$par
+ ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
+ ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
+ result <- append(result,
+ list(Bxy.est.mle = coef['x'],
+ Bxy.ci.upper.mle = ci.upper['x'],
+ Bxy.ci.lower.mle = ci.lower['x'],
+ Bzy.est.mle = coef['z'],
+ Bzy.ci.upper.mle = ci.upper['z'],
+ Bzy.ci.lower.mle = ci.lower['z']))
+
+
+ ## my implementatoin of liklihood based correction
+ mod.zhang <- zhang.mle.dv(df)
+ coef <- coef(mod.zhang)
+ ci <- confint(mod.zhang,method='quad')
+
+ result <- append(result,
+ list(Bxy.est.zhang = coef['Bxy'],
+ Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
+ Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
+ Bzy.est.zhang = coef['Bzy'],
+ Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
+ Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
+
+
+
+ # amelia says use normal distribution for binary variables.
+ amelia_result <- list(Bxy.est.amelia.full = NA,
+ Bxy.ci.upper.amelia.full = NA,
+ Bxy.ci.lower.amelia.full = NA,
+ Bzy.est.amelia.full = NA,
+ Bzy.ci.upper.amelia.full = NA,
+ Bzy.ci.lower.amelia.full = NA
+ )
+
+ tryCatch({
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
+ mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$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.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)
+
+ 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){
+
+ 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.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]))
- ## 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)
- mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
+ mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$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
))
+
+ 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)
+
+ ## 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'])
+ ## )
+
+
+
+ fischer.info <- NA
+ ci.upper <- NA
+ ci.lower <- NA
+
+ tryCatch({fischer.info <- solve(mod.caroll.lik$hessian)
+ ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
+ ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
+ },
+
+ error=function(e) {result[['error']] <- as.character(e)
+ })
+
+ coef <- mod.caroll.lik$par
+
+ 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']))
+
+ 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 %']))
+
## 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')
- (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
## 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