## 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)]
+ 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
-
- 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 == 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))
+ 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,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')
+ 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 Carolla
-zhang.mle.dv <- function(df){
+## 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)]
+## 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))
+## ## 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))
+## ## 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)
+## }
- ## 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))
+zhang.mle.dv <- function(df){
+ df.obs <- df[!is.na(y.obs)]
+ df.unobs <- df[is.na(y.obs)]
- lls <- colLogSumExps(rbind(lls.y.1, lls.y.0))
- ll <- ll + sum(lls)
- return(-ll)
+ 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=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))
+ 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
my.mle <- function(df){
accuracy <- df[,mean(w_pred==y)]
result <- append(result, list(accuracy=accuracy))
+ error.cor.x <- cor(df$x, df$w - df$x)
+ result <- append(result, list(error.cor.x = error.cor.x))
+ model.null <- glm(y~1, data=df,family=binomial(link='logit'))
(model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
+ (lik.ratio <- exp(logLik(model.true) - logLik(model.null)))
+
true.ci.Bxy <- confint(model.true)['x',]
true.ci.Bzy <- confint(model.true)['z',]
+
+ result <- append(result, list(lik.ratio=lik.ratio))
+
result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
Bzy.est.true=coef(model.true)['z'],
Bxy.ci.upper.true = true.ci.Bxy[2],
naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
- ## my implementatoin of liklihood based correction
+ ## my implementation of liklihood based correction
temp.df <- copy(df)
temp.df[,y:=y.obs]
Bzy.est.zhang = coef['Bzy'],
Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
-
+
+
# amelia says use normal distribution for binary variables.
tryCatch({
## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle
-run_simulation <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~x, truth_formula=x~z){
+run_simulation <- function(df, result, outcome_formula=y~x+z, proxy_formula=NULL, truth_formula=NULL){
accuracy <- df[,mean(w_pred==x)]
- result <- append(result, list(accuracy=accuracy))
-
+ accuracy.y0 <- df[y<=0,mean(w_pred==x)]
+ accuracy.y1 <- df[y>=0,mean(w_pred==x)]
+ cor.y.xi <- cor(df$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$z)))
(model.true <- lm(y ~ x + z, data=df))
true.ci.Bxy <- confint(model.true)['x',]
true.ci.Bzy <- confint(model.true)['z',]
tryCatch({
- amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
+ amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
projects / ml_measurement_error_public.git / blobdiff