library(bbmle)
library(matrixStats) # for numerically stable logsumexps
+source("pl_methods.R")
source("measerr_methods.R") ## for my more generic function.
## This uses the pseudolikelihood approach from Carroll page 349.
}
-
-## 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){
- nll <- function(B0=0, Bxy=0, Bzy=0, sigma_y=0.1, ppv=0.9, npv=0.9){
- df.obs <- df[!is.na(x.obs)]
- df.unobs <- df[is.na(x.obs)]
-
- ## fpr = 1 - TNR
- ### Problem: accounting for uncertainty in ppv / npv
-
- ll.w1x1.obs <- with(df.obs[(w_pred==1)], dbinom(x.obs,size=1,prob=ppv,log=T))
- ll.w0x0.obs <- with(df.obs[(w_pred==0)], dbinom(1-x.obs,size=1,prob=npv,log=T))
-
- ## 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)
- ll <- ll + sum(ll.w1x1.obs) + sum(ll.w0x0.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(lls.x.1, 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,ppv=0.00001, npv=0.00001),
- upper=list(sigma_y=Inf, B0=Inf, Bxy=Inf, Bzy=Inf, ppv=0.99999,npv=0.99999),method='L-BFGS-B')
- return(mlefit)
-}
-
-## this is equivalent to the pseudo-liklihood model from Carolla
-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)
-}
-
+
## This uses the likelihood approach from Carroll page 353.
## assumes that we have a good measurement error model
my.mle <- function(df){
return(mlefit)
}
-run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y){
+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)]
+ (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$w_pred))
+ result <- append(result, list(error.cor.x = error.cor.x,
+ error.cor.z = error.cor.z,
+ error.cor.y = error.cor.y))
+
+ model.null <- glm(y~1, data=df,family=binomial(link='logit'))
(model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
+ (lik.ratio <- exp(logLik(model.true) - logLik(model.null)))
+
true.ci.Bxy <- confint(model.true)['x',]
true.ci.Bzy <- confint(model.true)['z',]
+ result <- append(result, list(cor.xz=cor(df$x,df$z)))
+ result <- append(result, list(lik.ratio=lik.ratio))
+
result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
Bzy.est.true=coef(model.true)['z'],
Bxy.ci.upper.true = true.ci.Bxy[2],
naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
- ## my implementatoin of liklihood based correction
+ ## my implementation of liklihood based correction
temp.df <- copy(df)
temp.df[,y:=y.obs]
+
mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
- fisher.info <- solve(mod.caroll.lik$hessian)
+ fischer.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
+ 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'],
Bzy.ci.upper.mle = ci.upper['z'],
Bzy.ci.lower.mle = ci.lower['z']))
+ mod.caroll.profile.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, method='bbmle')
+ coef <- coef(mod.caroll.profile.lik)
+ ci <- confint(mod.caroll.profile.lik, method='spline')
+ ci.lower <- ci[,'2.5 %']
+ ci.upper <- ci[,'97.5 %']
+
+ result <- append(result,
+ list(Bxy.est.mle.profile = coef['x'],
+ Bxy.ci.upper.mle.profile = ci.upper['x'],
+ Bxy.ci.lower.mle.profile = ci.lower['x'],
+ Bzy.est.mle.profile = coef['z'],
+ Bzy.ci.upper.mle.profile = ci.upper['z'],
+ Bzy.ci.lower.mle.profile = ci.lower['z']))
## my implementatoin of liklihood based correction
mod.zhang <- zhang.mle.dv(df)
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$imputations, cite=FALSE)
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'),ords="y.obs")
+ mod.amelia.k <- zelig(y.obs~x+z, model='logit', data=amelia.out.k$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
- ))
-
+ 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){
- message("An error occurred:\n",e)
- result$error <- paste0(result$error,'\n', 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=w_pred~x, truth_formula=x~z){
+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)]
- result <- append(result, list(accuracy=accuracy))
-
+ 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',]
Bxy.ci.lower.naive = naive.ci.Bxy[1],
Bzy.ci.upper.naive = naive.ci.Bzy[2],
Bzy.ci.lower.naive = naive.ci.Bzy[1]))
-
- tryCatch({
- amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
- mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
- (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+ amelia_result <- list(
+ Bxy.est.amelia.full = NULL,
+ Bxy.ci.upper.amelia.full = NULL,
+ Bxy.ci.lower.amelia.full = NULL,
+ Bzy.est.amelia.full = NULL,
+ Bzy.ci.upper.amelia.full = NULL,
+ Bzy.ci.lower.amelia.full = NULL
+ )
- est.x.mi <- coefse['x.obs','Estimate']
- est.x.se <- coefse['x.obs','Std.Error']
- result <- append(result,
- list(Bxy.est.amelia.full = est.x.mi,
- Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
- Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
- ))
+ tryCatch({
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
+ mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+ (coefse <- combine_coef_se(mod.amelia.k))
- est.z.mi <- coefse['z','Estimate']
- est.z.se <- coefse['z','Std.Error']
+ 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']
- 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
- ))
+ 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){
- message("An error occurred:\n",e)
- result$error <-paste0(result$error,'\n', 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]
- 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$hessian)
+ mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='optim')
+ fischer.info <- solve(mod.caroll.lik$hessian)
coef <- mod.caroll.lik$par
- ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
- ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
-
-
- result <- append(result,
- list(Bxy.est.mle = coef['x'],
- Bxy.ci.upper.mle = ci.upper['x'],
- Bxy.ci.lower.mle = ci.lower['x'],
- Bzy.est.mle = coef['z'],
- Bzy.ci.upper.mle = ci.upper['z'],
- Bzy.ci.lower.mle = ci.lower['z']))
+ ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
+ ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
+
+ mle_result <- list(Bxy.est.mle = coef['x'],
+ Bxy.ci.upper.mle = ci.upper['x'],
+ Bxy.ci.lower.mle = ci.lower['x'],
+ Bzy.est.mle = coef['z'],
+ Bzy.ci.upper.mle = ci.upper['z'],
+ Bzy.ci.lower.mle = ci.lower['z'])
+ },
+ error=function(e) {result[['error']] <- as.character(e)
+ })
+
+ result <- append(result, mle_result)
+ mle_result_proflik <- list(Bxy.est.mle.profile = NULL,
+ Bxy.ci.upper.mle.profile = NULL,
+ Bxy.ci.lower.mle.profile = NULL,
+ Bzy.est.mle.profile = NULL,
+ Bzy.ci.upper.mle.profile = NULL,
+ Bzy.ci.lower.mle.profile = NULL)
+
+ tryCatch({
+ ## confint_method == 'bbmle'
+ mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='bbmle')
+ coef <- coef(mod.caroll.lik)
+ ci <- confint(mod.caroll.lik, method='spline')
+ ci.lower <- ci[,'2.5 %']
+ ci.upper <- ci[,'97.5 %']
+
+ mle_result_proflik <- list(Bxy.est.mle.profile = coef['x'],
+ Bxy.ci.upper.mle.profile = ci.upper['x'],
+ Bxy.ci.lower.mle.profile = ci.lower['x'],
+ Bzy.est.mle.profile = coef['z'],
+ Bzy.ci.upper.mle.profile = ci.upper['z'],
+ Bzy.ci.lower.mle.profile = ci.lower['z'])
},
- error = function(e){
- message("An error occurred:\n",e)
- result$error <- paste0(result$error,'\n', e)
+ error=function(e) {result[['error']] <- as.character(e)
})
+
+ result <- append(result, mle_result_proflik)
- tryCatch({
+ zhang_result <- list(Bxy.est.mle.zhang = NULL,
+ Bxy.ci.upper.mle.zhang = NULL,
+ Bxy.ci.lower.mle.zhang = NULL,
+ Bzy.est.mle.zhang = NULL,
+ Bzy.ci.upper.mle.zhang = NULL,
+ Bzy.ci.lower.mle.zhang = NULL)
- mod.zhang.lik <- zhang.mle.iv(df)
- coef <- coef(mod.zhang.lik)
- ci <- confint(mod.zhang.lik,method='quad')
- result <- append(result,
- list(Bxy.est.zhang = coef['Bxy'],
- Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
- Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
- Bzy.est.zhang = coef['Bzy'],
- Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
- Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
+ tryCatch({
+ mod.zhang.lik <- zhang.mle.iv(df)
+ coef <- coef(mod.zhang.lik)
+ ci <- confint(mod.zhang.lik,method='quad')
+ zhang_result <- list(Bxy.est.zhang = coef['Bxy'],
+ Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
+ Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
+ Bzy.est.zhang = coef['Bzy'],
+ Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
+ Bzy.ci.lower.zhang = ci['Bzy','2.5 %'])
},
-
- error = function(e){
- message("An error occurred:\n",e)
- result$error <- paste0(result$error,'\n', e)
+ error=function(e) {result[['error']] <- as.character(e)
})
+ result <- append(result, zhang_result)
## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
Bzy.ci.lower.gmm = gmm.res$confint[2,1]))
- 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'])
- )
-
- (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)
- }
- )
+ ## 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'])
+ ## )
+
+ ## (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