Nathan TeBlunthuis
82fe7b0f48
+ add pl_methods.R + update makefile + fix bug in 02_indep_differential.R + start documenting robustness checks in robustness_check_notes.md
85 lines
2.8 KiB
R
85 lines
2.8 KiB
R
library(stats4)
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library(bbmle)
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library(matrixStats)
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zhang.mle.dv <- function(df){
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df.obs <- df[!is.na(y.obs)]
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df.unobs <- df[is.na(y.obs)]
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fp <- df.obs[(w_pred==1) & (y.obs != w_pred),.N]
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tn <- df.obs[(w_pred == 0) & (y.obs == w_pred),.N]
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fpr <- fp / (fp+tn)
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fn <- df.obs[(w_pred==0) & (y.obs != w_pred), .N]
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tp <- df.obs[(w_pred==1) & (y.obs == w_pred),.N]
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fnr <- fn / (fn+tp)
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nll <- function(B0=0, Bxy=0, Bzy=0){
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## observed case
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ll.y.obs <- vector(mode='numeric', length=nrow(df.obs))
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ll.y.obs[df.obs$y.obs==1] <- with(df.obs[y.obs==1], plogis(B0 + Bxy * x + Bzy * z,log=T))
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ll.y.obs[df.obs$y.obs==0] <- with(df.obs[y.obs==0], plogis(B0 + Bxy * x + Bzy * z,log=T,lower.tail=FALSE))
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ll <- sum(ll.y.obs)
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pi.y.1 <- with(df.unobs,plogis(B0 + Bxy * x + Bzy*z, log=T))
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#pi.y.0 <- with(df.unobs,plogis(B0 + Bxy * x + Bzy*z, log=T,lower.tail=FALSE))
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lls <- with(df.unobs, colLogSumExps(rbind(w_pred * colLogSumExps(rbind(log(fpr), log(1 - fnr - fpr)+pi.y.1)),
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(1-w_pred) * (log(1-fpr) - exp(log(1-fnr-fpr)+pi.y.1)))))
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ll <- ll + sum(lls)
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print(paste0(B0,Bxy,Bzy))
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print(ll)
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return(-ll)
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}
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mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6),method='L-BFGS-B',lower=c(B0=-Inf, Bxy=-Inf, Bzy=-Inf),
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upper=c(B0=Inf, Bxy=Inf, Bzy=Inf))
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return(mlefit)
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}
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## model from Zhang's arxiv paper, with predictions for y
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## Zhang got this model from Hausman 1998
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zhang.mle.iv <- function(df){
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df.obs <- df[!is.na(x.obs)]
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df.unobs <- df[is.na(x.obs)]
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tn <- df.obs[(w_pred == 0) & (x.obs == w_pred),.N]
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fn <- df.obs[(w_pred==0) & (x.obs==1), .N]
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npv <- tn / (tn + fn)
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tp <- df.obs[(w_pred==1) & (x.obs == w_pred),.N]
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fp <- df.obs[(w_pred==1) & (x.obs == 0),.N]
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ppv <- tp / (tp + fp)
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nll <- function(B0=0, Bxy=0, Bzy=0, sigma_y=0.1){
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## fpr = 1 - TNR
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### Problem: accounting for uncertainty in ppv / npv
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## fnr = 1 - TPR
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ll.y.obs <- with(df.obs, dnorm(y, B0 + Bxy * x + Bzy * z, sd=sigma_y,log=T))
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ll <- sum(ll.y.obs)
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# unobserved case; integrate out x
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ll.x.1 <- with(df.unobs, dnorm(y, B0 + Bxy + Bzy * z, sd = sigma_y, log=T))
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ll.x.0 <- with(df.unobs, dnorm(y, B0 + Bzy * z, sd = sigma_y,log=T))
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## case x == 1
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lls.x.1 <- colLogSumExps(rbind(log(ppv) + ll.x.1, log(1-ppv) + ll.x.0))
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## case x == 0
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lls.x.0 <- colLogSumExps(rbind(log(1-npv) + ll.x.1, log(npv) + ll.x.0))
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lls <- colLogSumExps(rbind(df.unobs$w_pred * lls.x.1, (1-df.unobs$w_pred) * lls.x.0))
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ll <- ll + sum(lls)
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return(-ll)
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}
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mlefit <- mle2(minuslogl = nll, control=list(maxit=1e6), lower=list(sigma_y=0.0001, B0=-Inf, Bxy=-Inf, Bzy=-Inf),
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upper=list(sigma_y=Inf, B0=Inf, Bxy=Inf, Bzy=Inf),method='L-BFGS-B')
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return(mlefit)
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}
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