435 lines
18 KiB
R
435 lines
18 KiB
R
library(predictionError)
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library(mecor)
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options(amelia.parallel="no",
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amelia.ncpus=1)
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library(Amelia)
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library(Zelig)
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library(bbmle)
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library(matrixStats) # for numerically stable logsumexps
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source("pl_methods.R")
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source("measerr_methods.R") ## for my more generic function.
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## This uses the pseudolikelihood approach from Carroll page 349.
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## assumes MAR
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## assumes differential error, but that only depends on Y
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## inefficient, because pseudolikelihood
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## This uses the pseudo-likelihood approach from Carroll page 346.
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my.pseudo.mle <- function(df){
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p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
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p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
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nll <- function(B0, Bxy, Bzy){
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pw <- vector(mode='numeric',length=nrow(df))
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dfw1 <- df[w_pred==1]
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dfw0 <- df[w_pred==0]
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pw[df$w_pred==1] <- plogis(B0 + Bxy * dfw1$x + Bzy * dfw1$z, log=T)
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pw[df$w_pred==0] <- plogis(B0 + Bxy * dfw0$x + Bzy * dfw0$z, lower.tail=FALSE, log=T)
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probs <- colLogSumExps(rbind(log(1 - p0.est), log(p1.est + p0.est - 1) + pw))
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return(-1*sum(probs))
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}
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mlefit <- mle2(minuslogl = nll, start = list(B0=0.0, Bxy=0.0, Bzy=0.0), control=list(maxit=1e6),method='L-BFGS-B')
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return(mlefit)
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}
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## This uses the likelihood approach from Carroll page 353.
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## assumes that we have a good measurement error model
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my.mle <- function(df){
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## liklihood for observed responses
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nll <- function(B0, Bxy, Bzy, gamma0, gamma_y, gamma_z, gamma_yz){
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df.obs <- df[!is.na(y.obs)]
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yobs0 <- df.obs$y==0
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yobs1 <- df.obs$y==1
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p.y.obs <- vector(mode='numeric', length=nrow(df.obs))
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p.y.obs[yobs1] <- plogis(B0 + Bxy * df.obs[yobs1]$x + Bzy*df.obs[yobs1]$z,log=T)
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p.y.obs[yobs0] <- plogis(B0 + Bxy * df.obs[yobs0]$x + Bzy*df.obs[yobs0]$z,lower.tail=FALSE,log=T)
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wobs0 <- df.obs$w_pred==0
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wobs1 <- df.obs$w_pred==1
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p.w.obs <- vector(mode='numeric', length=nrow(df.obs))
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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)
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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)
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p.obs <- p.w.obs + p.y.obs
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df.unobs <- df[is.na(y.obs)]
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p.unobs.0 <- vector(mode='numeric',length=nrow(df.unobs))
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p.unobs.1 <- vector(mode='numeric',length=nrow(df.unobs))
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wunobs.0 <- df.unobs$w_pred == 0
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wunobs.1 <- df.unobs$w_pred == 1
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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)
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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)
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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]$z, log=T)
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p.unobs.1[wunobs.0] <- plogis(B0 + Bxy * df.unobs[wunobs.0]$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)
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p.unobs <- colLogSumExps(rbind(p.unobs.1, p.unobs.0))
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p <- c(p.obs, p.unobs)
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return(-1*(sum(p)))
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}
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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')
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return(mlefit)
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}
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run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y){
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(accuracy <- df[,mean(w_pred==y)])
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result <- append(result, list(accuracy=accuracy))
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(error.cor.z <- cor(df$z, df$y - df$w_pred))
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(error.cor.x <- cor(df$x, df$y - df$w_pred))
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(error.cor.y <- cor(df$y, df$y - df$w_pred))
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result <- append(result, list(error.cor.x = error.cor.x,
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error.cor.z = error.cor.z,
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error.cor.y = error.cor.y))
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model.null <- glm(y~1, data=df,family=binomial(link='logit'))
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(model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
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(lik.ratio <- exp(logLik(model.true) - logLik(model.null)))
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true.ci.Bxy <- confint(model.true)['x',]
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true.ci.Bzy <- confint(model.true)['z',]
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result <- append(result, list(cor.xz=cor(df$x,df$z)))
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result <- append(result, list(lik.ratio=lik.ratio))
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result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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Bzy.est.true=coef(model.true)['z'],
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Bxy.ci.upper.true = true.ci.Bxy[2],
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Bxy.ci.lower.true = true.ci.Bxy[1],
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Bzy.ci.upper.true = true.ci.Bzy[2],
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Bzy.ci.lower.true = true.ci.Bzy[1]))
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(model.feasible <- glm(y.obs~x+z,data=df,family=binomial(link='logit')))
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feasible.ci.Bxy <- confint(model.feasible)['x',]
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result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
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Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
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Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
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feasible.ci.Bzy <- confint(model.feasible)['z',]
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result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
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Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
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Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
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(model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))
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naive.ci.Bxy <- confint(model.naive)['x',]
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naive.ci.Bzy <- confint(model.naive)['z',]
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result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
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Bzy.est.naive=coef(model.naive)['z'],
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Bxy.ci.upper.naive = naive.ci.Bxy[2],
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Bxy.ci.lower.naive = naive.ci.Bxy[1],
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Bzy.ci.upper.naive = naive.ci.Bzy[2],
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Bzy.ci.lower.naive = naive.ci.Bzy[1]))
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(model.naive.cont <- lm(w~x+z, data=df))
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naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
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naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
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## my implementation of liklihood based correction
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temp.df <- copy(df)
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temp.df[,y:=y.obs]
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mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
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fischer.info <- solve(mod.caroll.lik$hessian)
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coef <- mod.caroll.lik$par
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ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
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ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
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result <- append(result,
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list(Bxy.est.mle = coef['x'],
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Bxy.ci.upper.mle = ci.upper['x'],
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Bxy.ci.lower.mle = ci.lower['x'],
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Bzy.est.mle = coef['z'],
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Bzy.ci.upper.mle = ci.upper['z'],
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Bzy.ci.lower.mle = ci.lower['z']))
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## my implementatoin of liklihood based correction
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mod.zhang <- zhang.mle.dv(df)
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coef <- coef(mod.zhang)
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ci <- confint(mod.zhang,method='quad')
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result <- append(result,
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list(Bxy.est.zhang = coef['Bxy'],
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Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
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Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
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Bzy.est.zhang = coef['Bzy'],
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Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
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Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
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# amelia says use normal distribution for binary variables.
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amelia_result <- list(Bxy.est.amelia.full = NA,
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Bxy.ci.upper.amelia.full = NA,
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Bxy.ci.lower.amelia.full = NA,
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Bzy.est.amelia.full = NA,
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Bzy.ci.upper.amelia.full = NA,
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Bzy.ci.lower.amelia.full = NA
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)
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tryCatch({
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amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
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mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
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(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
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est.x.mi <- coefse['x','Estimate']
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est.x.se <- coefse['x','Std.Error']
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est.z.mi <- coefse['z','Estimate']
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est.z.se <- coefse['z','Std.Error']
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amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
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Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
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Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
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Bzy.est.amelia.full = est.z.mi,
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Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
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Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
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)
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},
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error = function(e){
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result[['error']] <- e}
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)
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result <- append(result,amelia_result)
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return(result)
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}
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## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle
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run_simulation <- function(df, result, outcome_formula=y~x+z, proxy_formula=NULL, truth_formula=NULL){
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accuracy <- df[,mean(w_pred==x)]
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accuracy.y0 <- df[y<=0,mean(w_pred==x)]
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accuracy.y1 <- df[y>=0,mean(w_pred==x)]
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cor.y.xi <- cor(df$x - df$w_pred, df$y)
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fnr <- df[w_pred==0,mean(w_pred!=x)]
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fnr.y0 <- df[(w_pred==0) & (y<=0),mean(w_pred!=x)]
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fnr.y1 <- df[(w_pred==0) & (y>=0),mean(w_pred!=x)]
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fpr <- df[w_pred==1,mean(w_pred!=x)]
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fpr.y0 <- df[(w_pred==1) & (y<=0),mean(w_pred!=x)]
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fpr.y1 <- df[(w_pred==1) & (y>=0),mean(w_pred!=x)]
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cor.resid.w_pred <- cor(resid(lm(y~x+z,df)),df$w_pred)
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result <- append(result, list(accuracy=accuracy,
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accuracy.y0=accuracy.y0,
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accuracy.y1=accuracy.y1,
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cor.y.xi=cor.y.xi,
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fnr=fnr,
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fnr.y0=fnr.y0,
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fnr.y1=fnr.y1,
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fpr=fpr,
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fpr.y0=fpr.y0,
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fpr.y1=fpr.y1,
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cor.resid.w_pred=cor.resid.w_pred
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))
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result <- append(result, list(cor.xz=cor(df$x,df$z)))
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(model.true <- lm(y ~ x + z, data=df))
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true.ci.Bxy <- confint(model.true)['x',]
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true.ci.Bzy <- confint(model.true)['z',]
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result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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Bzy.est.true=coef(model.true)['z'],
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Bxy.ci.upper.true = true.ci.Bxy[2],
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Bxy.ci.lower.true = true.ci.Bxy[1],
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Bzy.ci.upper.true = true.ci.Bzy[2],
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Bzy.ci.lower.true = true.ci.Bzy[1]))
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(model.feasible <- lm(y~x.obs+z,data=df))
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feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
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result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
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Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
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Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
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feasible.ci.Bzy <- confint(model.feasible)['z',]
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result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
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Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
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Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
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(model.naive <- lm(y~w_pred+z, data=df))
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naive.ci.Bxy <- confint(model.naive)['w_pred',]
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naive.ci.Bzy <- confint(model.naive)['z',]
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result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'],
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Bzy.est.naive=coef(model.naive)['z'],
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Bxy.ci.upper.naive = naive.ci.Bxy[2],
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Bxy.ci.lower.naive = naive.ci.Bxy[1],
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Bzy.ci.upper.naive = naive.ci.Bzy[2],
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Bzy.ci.lower.naive = naive.ci.Bzy[1]))
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amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
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mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
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(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
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est.x.mi <- coefse['x.obs','Estimate']
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est.x.se <- coefse['x.obs','Std.Error']
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result <- append(result,
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list(Bxy.est.amelia.full = est.x.mi,
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Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
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Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
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))
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est.z.mi <- coefse['z','Estimate']
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est.z.se <- coefse['z','Std.Error']
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result <- append(result,
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list(Bzy.est.amelia.full = est.z.mi,
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Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
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Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
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))
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temp.df <- copy(df)
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temp.df <- temp.df[,x:=x.obs]
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mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
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## tryCatch({
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## mod.calibrated.mle <- mecor(y ~ MeasError(w_pred, reference = x.obs) + z, df, B=400, method='efficient')
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## (mod.calibrated.mle)
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## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
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## result <- append(result, list(
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## Bxy.est.mecor = mecor.ci['Estimate'],
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## Bxy.ci.upper.mecor = mecor.ci['UCI'],
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## Bxy.ci.lower.mecor = mecor.ci['LCI'])
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## )
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fischer.info <- NA
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ci.upper <- NA
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ci.lower <- NA
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tryCatch({fischer.info <- solve(mod.caroll.lik$hessian)
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ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
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ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
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},
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error=function(e) {result[['error']] <- as.character(e)
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})
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coef <- mod.caroll.lik$par
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result <- append(result,
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list(Bxy.est.mle = coef['x'],
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Bxy.ci.upper.mle = ci.upper['x'],
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Bxy.ci.lower.mle = ci.lower['x'],
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Bzy.est.mle = coef['z'],
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Bzy.ci.upper.mle = ci.upper['z'],
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Bzy.ci.lower.mle = ci.lower['z']))
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mod.zhang.lik <- zhang.mle.iv(df)
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coef <- coef(mod.zhang.lik)
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ci <- confint(mod.zhang.lik,method='quad')
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result <- append(result,
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list(Bxy.est.zhang = coef['Bxy'],
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Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
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Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
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Bzy.est.zhang = coef['Bzy'],
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Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
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Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
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## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
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## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
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## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
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## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
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## est.x.mi <- coefse['x.obs','Estimate']
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## est.x.se <- coefse['x.obs','Std.Error']
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## result <- append(result,
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## list(Bxy.est.amelia.nok = est.x.mi,
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## Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
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## Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
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## ))
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|
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## est.g.mi <- coefse['g','Estimate']
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## est.g.se <- coefse['g','Std.Error']
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|
|
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## result <- append(result,
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## list(Bgy.est.amelia.nok = est.g.mi,
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## Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
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## Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
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## ))
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|
|
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N <- nrow(df)
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m <- nrow(df[!is.na(x.obs)])
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p <- v <- train <- rep(0,N)
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M <- m
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p[(M+1):(N)] <- 1
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|
v[1:(M)] <- 1
|
|
df <- df[order(x.obs)]
|
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y <- df[,y]
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x <- df[,x.obs]
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z <- df[,z]
|
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w <- df[,w_pred]
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# gmm gets pretty close
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|
(gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))
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|
|
|
result <- append(result,
|
|
list(Bxy.est.gmm = gmm.res$beta[1,1],
|
|
Bxy.ci.upper.gmm = gmm.res$confint[1,2],
|
|
Bxy.ci.lower.gmm = gmm.res$confint[1,1],
|
|
gmm.ER_pval = gmm.res$ER_pval
|
|
))
|
|
|
|
result <- append(result,
|
|
list(Bzy.est.gmm = gmm.res$beta[2,1],
|
|
Bzy.ci.upper.gmm = gmm.res$confint[2,2],
|
|
Bzy.ci.lower.gmm = gmm.res$confint[2,1]))
|
|
|
|
|
|
## tryCatch({
|
|
## mod.calibrated.mle <- mecor(y ~ MeasError(w_pred, reference = x.obs) + z, df, B=400, method='efficient')
|
|
## (mod.calibrated.mle)
|
|
## (mecor.ci <- summary(mod.calibrated.mle)$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"))
|
|
|
|
## gc()
|
|
return(result)
|
|
}
|