library(stats4) library(bbmle) library(matrixStats) zhang.mle.dv <- function(df){ df.obs <- df[!is.na(y.obs)] df.unobs <- df[is.na(y.obs)] fp <- df.obs[(w_pred==1) & (y.obs != w_pred),.N] tn <- df.obs[(w_pred == 0) & (y.obs == w_pred),.N] fpr <- fp / (fp+tn) fn <- df.obs[(w_pred==0) & (y.obs != w_pred), .N] tp <- df.obs[(w_pred==1) & (y.obs == w_pred),.N] fnr <- fn / (fn+tp) 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.unobs,plogis(B0 + Bxy * x + Bzy*z, log=T)) #pi.y.0 <- with(df.unobs,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) * (log(1-fpr) - exp(log(1-fnr-fpr)+pi.y.1))))) ll <- ll + sum(lls) # print(paste0(B0,Bxy,Bzy)) # print(ll) return(-ll) } 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) } ## model from Zhang's arxiv paper, with predictions for y ## Zhang got this model from Hausman 1998 zhang.mle.iv <- function(df){ 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] fn <- df.obs[(w_pred==0) & (x.obs==1), .N] npv <- tn / (tn + fn) tp <- df.obs[(w_pred==1) & (x.obs == w_pred),.N] fp <- df.obs[(w_pred==1) & (x.obs == 0),.N] ppv <- tp / (tp + fp) nll <- function(B0=0, Bxy=0, Bzy=0, sigma_y=9){ ## fpr = 1 - TNR ### Problem: accounting for uncertainty in ppv / npv ## 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) # 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(df.unobs$w_pred * lls.x.1, (1-df.unobs$w_pred) * lls.x.0)) ll <- ll + sum(lls) } mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6), lower=list(sigma_y=0.00001, B0=-Inf, Bxy=-Inf, Bzy=-Inf), upper=list(sigma_y=Inf, B0=Inf, Bxy=Inf, Bzy=Inf),method='L-BFGS-B') return(mlefit) }