library(predictionError)
library(mecor)
options(amelia.parallel="no",
        amelia.ncpus=1)
library(Amelia)
library(Zelig)
library(bbmle)
library(matrixStats) # for numerically stable logsumexps

source("measerr_methods.R") ## for my more generic function.

## This uses the pseudolikelihood approach from Carroll page 349.
## assumes MAR
## assumes differential error, but that only depends on Y
## inefficient, because pseudolikelihood
    
## This uses the pseudo-likelihood approach from Carroll page 346.
my.pseudo.mle <- function(df){
    p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
    p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
    
    nll <- function(B0, Bxy, Bzy){

        pw <- vector(mode='numeric',length=nrow(df))
        dfw1 <- df[w_pred==1]
        dfw0 <- df[w_pred==0]
        pw[df$w_pred==1] <- plogis(B0 + Bxy * dfw1$x + Bzy * dfw1$z, log=T)
        pw[df$w_pred==0] <- plogis(B0 + Bxy * dfw0$x + Bzy * dfw0$z, lower.tail=FALSE, log=T)
        
        probs <- colLogSumExps(rbind(log(1 - p0.est), log(p1.est + p0.est - 1) + pw))
        return(-1*sum(probs))
    }
    
    mlefit <- mle2(minuslogl = nll, start = list(B0=0.0, Bxy=0.0, Bzy=0.0), control=list(maxit=1e6),method='L-BFGS-B')
    return(mlefit)

}


## model from Zhang's arxiv paper, with predictions for y
## Zhang got this model from Hausman 1998
### I think this is actually eqivalent to the pseudo.mle method
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]
    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

    ## 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)
}

## 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)]

##     ## 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))

##     ## 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)
## }

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]
    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=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){
    
    ## liklihood for observed responses
    nll <- function(B0, Bxy, Bzy, gamma0, gamma_y, gamma_z, gamma_yz){
        df.obs <- df[!is.na(y.obs)]
        yobs0 <- df.obs$y==0 
        yobs1 <- df.obs$y==1
        p.y.obs <- vector(mode='numeric', length=nrow(df.obs))
        
        p.y.obs[yobs1] <- plogis(B0 + Bxy * df.obs[yobs1]$x + Bzy*df.obs[yobs1]$z,log=T)
        p.y.obs[yobs0] <- plogis(B0 + Bxy * df.obs[yobs0]$x + Bzy*df.obs[yobs0]$z,lower.tail=FALSE,log=T)

        wobs0 <- df.obs$w_pred==0
        wobs1 <- df.obs$w_pred==1
        p.w.obs <- vector(mode='numeric', length=nrow(df.obs))

        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)
        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)
        
        p.obs <- p.w.obs + p.y.obs

        df.unobs <- df[is.na(y.obs)]

        p.unobs.0 <- vector(mode='numeric',length=nrow(df.unobs))
        p.unobs.1 <- vector(mode='numeric',length=nrow(df.unobs))

        wunobs.0 <- df.unobs$w_pred == 0
        wunobs.1 <- df.unobs$w_pred == 1
        
        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)

        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)

        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)

        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)

        p.unobs <- colLogSumExps(rbind(p.unobs.1, p.unobs.0))

        p <- c(p.obs, p.unobs)

        return(-1*(sum(p)))
    }

    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')

    return(mlefit)
}

run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y){

    accuracy <- df[,mean(w_pred==y)]
    result <- append(result, list(accuracy=accuracy))

    (model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
    true.ci.Bxy <- confint(model.true)['x',]
    true.ci.Bzy <- confint(model.true)['z',]

    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],
                                  Bxy.ci.lower.true = true.ci.Bxy[1],
                                  Bzy.ci.upper.true = true.ci.Bzy[2],
                                  Bzy.ci.lower.true = true.ci.Bzy[1]))
                                  
    (model.feasible <- glm(y.obs~x+z,data=df,family=binomial(link='logit')))

    feasible.ci.Bxy <- confint(model.feasible)['x',]
    result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
                                  Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
                                  Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))

    feasible.ci.Bzy <- confint(model.feasible)['z',]
    result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
                                  Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
                                  Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))

    (model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))

    naive.ci.Bxy <- confint(model.naive)['x',]
    naive.ci.Bzy <- confint(model.naive)['z',]

    result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
                                  Bzy.est.naive=coef(model.naive)['z'],
                                  Bxy.ci.upper.naive = naive.ci.Bxy[2],
                                  Bxy.ci.lower.naive = naive.ci.Bxy[1],
                                  Bzy.ci.upper.naive = naive.ci.Bzy[2],
                                  Bzy.ci.lower.naive = naive.ci.Bzy[1]))


    (model.naive.cont <- lm(w~x+z, data=df))
    naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
    naivecont.ci.Bzy <- confint(model.naive.cont)['z',]

    ## my implementation of liklihood based correction

    temp.df <- copy(df)
    temp.df[,y:=y.obs]
    mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
    fisher.info <- solve(mod.caroll.lik$hessian)
    coef <- mod.caroll.lik$par
    ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
    ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
    result <- append(result,
                     list(Bxy.est.mle = coef['x'],
                          Bxy.ci.upper.mle = ci.upper['x'],
                          Bxy.ci.lower.mle = ci.lower['x'],
                          Bzy.est.mle = coef['z'],
                          Bzy.ci.upper.mle = ci.upper['z'],
                          Bzy.ci.lower.mle = ci.lower['z']))


    ## my implementatoin of liklihood based correction
    mod.zhang <- zhang.mle.dv(df)
    coef <- coef(mod.zhang)
    ci <- confint(mod.zhang,method='quad')

    result <- append(result,
                     list(Bxy.est.zhang = coef['Bxy'],
                          Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
                          Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
                          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({
        amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
        mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
        (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
        est.x.mi <- coefse['x','Estimate']
        est.x.se <- coefse['x','Std.Error']
        result <- append(result,
                         list(Bxy.est.amelia.full = est.x.mi,
                              Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
                              Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
                              ))

        est.z.mi <- coefse['z','Estimate']
        est.z.se <- coefse['z','Std.Error']

        result <- append(result,
                         list(Bzy.est.amelia.full = est.z.mi,
                              Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
                              Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
                              ))

    },
    error = function(e){
        message("An error occurred:\n",e)
        result$error <- paste0(result$error,'\n', e)
    })


    return(result)

}


## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle 
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))

    (model.true <- lm(y ~ x + z, data=df))
    true.ci.Bxy <- confint(model.true)['x',]
    true.ci.Bzy <- confint(model.true)['z',]

    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],
                                  Bxy.ci.lower.true = true.ci.Bxy[1],
                                  Bzy.ci.upper.true = true.ci.Bzy[2],
                                  Bzy.ci.lower.true = true.ci.Bzy[1]))
                                  
    (model.feasible <- lm(y~x.obs+z,data=df))

    feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
    result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
                                  Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
                                  Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))

    feasible.ci.Bzy <- confint(model.feasible)['z',]
    result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
                                  Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
                                  Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))

    (model.naive <- lm(y~w_pred+z, data=df))
    
    naive.ci.Bxy <- confint(model.naive)['w_pred',]
    naive.ci.Bzy <- confint(model.naive)['z',]

    result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'],
                                  Bzy.est.naive=coef(model.naive)['z'],
                                  Bxy.ci.upper.naive = naive.ci.Bxy[2],
                                  Bxy.ci.lower.naive = naive.ci.Bxy[1],
                                  Bzy.ci.upper.naive = naive.ci.Bzy[2],
                                  Bzy.ci.lower.naive = naive.ci.Bzy[1]))
                                  

    tryCatch({
    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))

    est.x.mi <- coefse['x.obs','Estimate']
    est.x.se <- coefse['x.obs','Std.Error']
    result <- append(result,
                     list(Bxy.est.amelia.full = est.x.mi,
                          Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
                          Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
                          ))

    est.z.mi <- coefse['z','Estimate']
    est.z.se <- coefse['z','Std.Error']

    result <- append(result,
                     list(Bzy.est.amelia.full = est.z.mi,
                          Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
                          Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
                          ))

    },
    error = function(e){
        message("An error occurred:\n",e)
        result$error <-paste0(result$error,'\n', e)
    }
    )

    tryCatch({
        temp.df <- copy(df)
        temp.df <- temp.df[,x:=x.obs]
        mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
        fisher.info <- solve(mod.caroll.lik$hessian)
        coef <- mod.caroll.lik$par
        ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
        ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
        
        
        result <- append(result,
                         list(Bxy.est.mle = coef['x'],
                              Bxy.ci.upper.mle = ci.upper['x'],
                              Bxy.ci.lower.mle = ci.lower['x'],
                              Bzy.est.mle = coef['z'],
                              Bzy.ci.upper.mle = ci.upper['z'],
                              Bzy.ci.lower.mle = ci.lower['z']))
    },

    error = function(e){
        message("An error occurred:\n",e)
        result$error <- paste0(result$error,'\n', e)
    })

    tryCatch({

        mod.zhang.lik <- zhang.mle.iv(df)
        coef <- coef(mod.zhang.lik)
        ci <- confint(mod.zhang.lik,method='quad')
        result <- append(result,
                         list(Bxy.est.zhang = coef['Bxy'],
                              Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
                              Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
                              Bzy.est.zhang = coef['Bzy'],
                              Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
                              Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
    },

    error = function(e){
        message("An error occurred:\n",e)
        result$error <- paste0(result$error,'\n', e)
    })

    ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
    ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
    ## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
    ## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))

    ## est.x.mi <- coefse['x.obs','Estimate']
    ## est.x.se <- coefse['x.obs','Std.Error']
    ## result <- append(result,
    ##                  list(Bxy.est.amelia.nok = est.x.mi,
    ##                       Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
    ##                       Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
    ##                       ))

    ## est.g.mi <- coefse['g','Estimate']
    ## est.g.se <- coefse['g','Std.Error']

    ## result <- append(result,
    ##                  list(Bgy.est.amelia.nok = est.g.mi,
    ##                       Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
    ##                       Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
    ##                       ))

    N <- nrow(df)
    m <- nrow(df[!is.na(x.obs)])
    p <- v <- train <- rep(0,N)
    M <- m
    p[(M+1):(N)] <- 1
    v[1:(M)] <- 1
    df <- df[order(x.obs)]
    y <- df[,y]
    x <- df[,x.obs]
    z <- df[,z]
    w <- df[,w_pred]
    # gmm gets pretty close
    (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))

    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)
}