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=0.1){

    ## 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)
    return(-ll)
    }    
    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)
}