library(formula.tools)
library(matrixStats)
library(optimx)
library(bbmle)
## df: dataframe to model
## outcome_formula: formula for y | x, z
## outcome_family: family for y | x, z
## proxy_formula: formula for w | x, z, y 
## proxy_family: family for w | x, z, y
## truth_formula: formula for x | z
## truth_family: family for x | z

### ideal formulas for example 1
# test.fit.1 <- measerr_mle(df, y ~ x + z, gaussian(), w_pred ~ x, binomial(link='logit'), x ~ z)

### ideal formulas for example 2
# test.fit.2 <- measerr_mle(df, y ~ x + z, gaussian(), w_pred ~ x + z + y + y:x, binomial(link='logit'), x ~ z)


## outcome_formula <- y ~ x + z; proxy_formula <- w_pred ~ y + x + z + x:z + x:y + z:y 
measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='logit'), proxy_formula, proxy_family=binomial(link='logit'),method='optim'){

    nll <- function(params){
        df.obs <- model.frame(outcome_formula, df)
        proxy.variable <- all.vars(proxy_formula)[1]
        proxy.model.matrix <- model.matrix(proxy_formula, df)
        response.var <- all.vars(outcome_formula)[1]
        y.obs <- with(df.obs,eval(parse(text=response.var)))
        outcome.model.matrix <- model.matrix(outcome_formula, df.obs)

        param.idx <- 1
        n.outcome.model.covars <- dim(outcome.model.matrix)[2]
        outcome.params <- params[param.idx:n.outcome.model.covars]
        param.idx <- param.idx + n.outcome.model.covars

        if((outcome_family$family == "binomial") & (outcome_family$link == 'logit')){
            ll.y.obs <- vector(mode='numeric', length=length(y.obs))
            ll.y.obs[y.obs==1] <- plogis(outcome.params %*% t(outcome.model.matrix[y.obs==1,]),log=TRUE)
            ll.y.obs[y.obs==0] <- plogis(outcome.params %*% t(outcome.model.matrix[y.obs==0,]),log=TRUE,lower.tail=FALSE)
        }

        df.obs <- model.frame(proxy_formula,df)
        n.proxy.model.covars <- dim(proxy.model.matrix)[2]
        proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]

        param.idx <- param.idx + n.proxy.model.covars
        proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))

        if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
            ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
            ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
            ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
        }

        ll.obs <- sum(ll.y.obs + ll.w.obs)

        df.unobs <- df[is.na(df[[response.var]])]
        df.unobs.y1 <- copy(df.unobs)
        df.unobs.y1[[response.var]] <- 1
        df.unobs.y0 <- copy(df.unobs)
        df.unobs.y0[[response.var]] <- 0
        
        ## integrate out y
        outcome.model.matrix.y1 <- model.matrix(outcome_formula, df.unobs.y1)

        if((outcome_family$family == "binomial") & (outcome_family$link == 'logit')){
            ll.y.unobs.1 <- vector(mode='numeric', length=dim(outcome.model.matrix.y1)[1])
            ll.y.unobs.0 <- vector(mode='numeric', length=dim(outcome.model.matrix.y1)[1])
            ll.y.unobs.1 <- plogis(outcome.params %*% t(outcome.model.matrix.y1),log=TRUE)
            ll.y.unobs.0 <- plogis(outcome.params %*% t(outcome.model.matrix.y1),log=TRUE,lower.tail=FALSE)
        }

        proxy.model.matrix.y1 <- model.matrix(proxy_formula, df.unobs.y1)
        proxy.model.matrix.y0 <- model.matrix(proxy_formula, df.unobs.y0)
        proxy.unobs <- with(df.unobs, eval(parse(text=proxy.variable)))

        if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
            ll.w.unobs.1 <- vector(mode='numeric',length=dim(proxy.model.matrix.y1)[1])
            ll.w.unobs.0 <- vector(mode='numeric',length=dim(proxy.model.matrix.y0)[1])
            ll.w.unobs.1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.y1[proxy.unobs==1,]),log=TRUE)
            ll.w.unobs.1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.y1[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)

            ll.w.unobs.0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.y0[proxy.unobs==1,]),log=TRUE)
            ll.w.unobs.0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.y0[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
        }

        ll.unobs.1 <- ll.y.unobs.1 + ll.w.unobs.1
        ll.unobs.0 <- ll.y.unobs.0 + ll.w.unobs.0
        ll.unobs <- sum(colLogSumExps(rbind(ll.unobs.1,ll.unobs.0)))
        ll <- ll.unobs + ll.obs
        return(-ll)
    }
    
    params <- colnames(model.matrix(outcome_formula,df))
    lower <- rep(-Inf, length(params))
    proxy.params <- colnames(model.matrix(proxy_formula, df))
    params <- c(params, paste0('proxy_',proxy.params))
    lower <- c(lower, rep(-Inf, length(proxy.params)))
    start <- rep(0.1,length(params))
    names(start) <- params
    
    if(method=='optim'){
        fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
    } else {
        quoted.names <- gsub("[\\(\\)]",'',names(start))
        print(quoted.names)
        text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(nll(params))}")

        measerr_mle_nll <- eval(parse(text=text))
        names(start) <- quoted.names
        names(lower) <- quoted.names
        fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
    }
    return(fit)
}


measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit'),method='optim'){

    df.obs <- model.frame(outcome_formula, df)
    response.var <- all.vars(outcome_formula)[1]
    proxy.variable <- all.vars(proxy_formula)[1]
    truth.variable <- all.vars(truth_formula)[1]
    outcome.model.matrix <- model.matrix(outcome_formula, df)
    proxy.model.matrix <- model.matrix(proxy_formula, df)
    y.obs <- with(df.obs,eval(parse(text=response.var)))

    measerr_mle_nll <- function(params){
        param.idx <- 1
        n.outcome.model.covars <- dim(outcome.model.matrix)[2]
        outcome.params <- params[param.idx:n.outcome.model.covars]
        param.idx <- param.idx + n.outcome.model.covars

        ## likelihood for the fully observed data 
        if(outcome_family$family == "gaussian"){
            sigma.y <- params[param.idx]
            param.idx <- param.idx + 1
                                        #  outcome_formula likelihood using linear regression
            ll.y.obs <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix),sd=sigma.y, log=TRUE)
        }
        
        df.obs <- model.frame(proxy_formula,df)
        n.proxy.model.covars <- dim(proxy.model.matrix)[2]
        proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
        param.idx <- param.idx + n.proxy.model.covars
        proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))

        if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
            ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])

                                        # proxy_formula likelihood using logistic regression
            ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
            ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
        }

        df.obs <- model.frame(truth_formula, df)

        truth.obs <- with(df.obs, eval(parse(text=truth.variable)))
        truth.model.matrix <- model.matrix(truth_formula,df)
        n.truth.model.covars <- dim(truth.model.matrix)[2]
        
        truth.params <- params[param.idx:(n.truth.model.covars + param.idx - 1)]

        if( (truth_family$family=="binomial") & (truth_family$link=='logit')){
            ll.x.obs <- vector(mode='numeric',length=dim(truth.model.matrix)[1])

                                        # truth_formula likelihood using logistic regression
            ll.x.obs[truth.obs==1] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==1,]),log=TRUE)
            ll.x.obs[truth.obs==0] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==0,]),log=TRUE, lower.tail=FALSE)
        }
        
                                        # add the three likelihoods
        ll.obs <- sum(ll.y.obs + ll.w.obs + ll.x.obs)

        ## likelihood for the predicted data
        ## integrate out the "truth" variable. 
        
        if(truth_family$family=='binomial'){
            df.unobs <- df[is.na(eval(parse(text=truth.variable)))]
            df.unobs.x1 <- copy(df.unobs)
            df.unobs.x1[,'x'] <- 1
            df.unobs.x0 <- copy(df.unobs)
            df.unobs.x0[,'x'] <- 0
            outcome.unobs <- with(df.unobs, eval(parse(text=response.var)))
            
            outcome.model.matrix.x0 <- model.matrix(outcome_formula, df.unobs.x0)
            outcome.model.matrix.x1 <- model.matrix(outcome_formula, df.unobs.x1)
            if(outcome_family$family=="gaussian"){

                                        # likelihood of outcome
                ll.y.x0 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x0), sd=sigma.y, log=TRUE)
                ll.y.x1 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x1), sd=sigma.y, log=TRUE)
            }

            if( (proxy_family$family=='binomial') & (proxy_family$link=='logit')){

                proxy.model.matrix.x0 <- model.matrix(proxy_formula, df.unobs.x0)
                proxy.model.matrix.x1 <- model.matrix(proxy_formula, df.unobs.x1)
                proxy.unobs <- df.unobs[[proxy.variable]]
                ll.w.x0 <- vector(mode='numeric', length=dim(df.unobs)[1])
                ll.w.x1 <- vector(mode='numeric', length=dim(df.unobs)[1])

                                        # likelihood of proxy
                ll.w.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==1,]), log=TRUE)
                ll.w.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==1,]), log=TRUE)

                ll.w.x0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
                ll.w.x1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
            }

            if(truth_family$link=='logit'){
                truth.model.matrix <- model.matrix(truth_formula, df.unobs.x0)
                                        # likelihood of truth
                ll.x.x1 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE)
                ll.x.x0 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE, lower.tail=FALSE)
            }
        }

        ll.x0 <- ll.y.x0 + ll.w.x0 + ll.x.x0
        ll.x1 <- ll.y.x1 + ll.w.x1 + ll.x.x1
        ll.unobs <- sum(colLogSumExps(rbind(ll.x0, ll.x1)))
        return(-(ll.unobs + ll.obs))
    }
    
    outcome.params <- colnames(model.matrix(outcome_formula,df))
    lower <- rep(-Inf, length(outcome.params))

    if(outcome_family$family=='gaussian'){
        params <- c(outcome.params, 'sigma_y')
        lower <- c(lower, 0.00001)
    } else {
        params <- outcome.params
    }
    
    proxy.params <- colnames(model.matrix(proxy_formula, df))
    params <- c(params, paste0('proxy_',proxy.params))
    lower <- c(lower, rep(-Inf, length(proxy.params)))

    truth.params <- colnames(model.matrix(truth_formula, df))
    params <- c(params, paste0('truth_', truth.params))
    lower <- c(lower, rep(-Inf, length(truth.params)))
    start <- rep(0.1,length(params))
    names(start) <- params

    if(method=='optim'){
        fit <- optim(start, fn = measerr_mle_nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
    } else { # method='mle2'
                
        quoted.names <- gsub("[\\(\\)]",'',names(start))

        text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(measerr_mle_nll(params))}")

        measerr_mle_nll_mle <- eval(parse(text=text))
        names(start) <- quoted.names
        names(lower) <- quoted.names
        fit <- mle2(minuslogl=measerr_mle_nll_mle, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
    }

    return(fit)
}

## Experimental, but probably works. 
measerr_irr_mle <- function(df, outcome_formula, outcome_family=gaussian(), coder_formulas=list(x.obs.0~x, x.obs.1~x), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit'),method='optim'){

    ### in this scenario, the ground truth also has measurement error, but we have repeated measures for it. 
    # this time we never get to observe the true X
    outcome.model.matrix <- model.matrix(outcome_formula, df)
    proxy.model.matrix <- model.matrix(proxy_formula, df)
    response.var <- all.vars(outcome_formula)[1]
    proxy.var <- all.vars(proxy_formula)[1]
    param.var <- all.vars(truth_formula)[1]
    truth.var<- all.vars(truth_formula)[1]
    y <- with(df,eval(parse(text=response.var)))

    nll <- function(params){
        param.idx <- 1
        n.outcome.model.covars <- dim(outcome.model.matrix)[2]
        outcome.params <- params[param.idx:n.outcome.model.covars]
        param.idx <- param.idx + n.outcome.model.covars


        if(outcome_family$family == "gaussian"){
            sigma.y <- params[param.idx]
            param.idx <- param.idx + 1
        }


        n.proxy.model.covars <- dim(proxy.model.matrix)[2]
        proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
        param.idx <- param.idx + n.proxy.model.covars
        
        df.temp <- copy(df)

        if((truth_family$family == "binomial")
           & (truth_family$link=='logit')){
            integrate.grid <- expand.grid(replicate(1 + length(coder_formulas), c(0,1), simplify=FALSE))
            ll.parts <- matrix(nrow=nrow(df),ncol=nrow(integrate.grid))
            for(i in 1:nrow(integrate.grid)){
                # setup the dataframe for this row
                row <- integrate.grid[i,]

                df.temp[[param.var]] <- row[[1]]
                ci <- 2
                for(coder_formula in coder_formulas){
                    coder.var <- all.vars(coder_formula)[1]
                    df.temp[[coder.var]] <- row[[ci]]
                    ci <- ci + 1 
                }
                
                outcome.model.matrix <- model.matrix(outcome_formula, df.temp)                
                if(outcome_family$family == "gaussian"){
                    ll.y <- dnorm(y, outcome.params %*% t(outcome.model.matrix), sd=sigma.y, log=TRUE)
                }

                if(proxy_family$family=="binomial" & (proxy_family$link=='logit')){
                    proxy.model.matrix <- model.matrix(proxy_formula, df.temp)
                    ll.w <- vector(mode='numeric', length=dim(proxy.model.matrix)[1])
                    proxyvar <- with(df.temp,eval(parse(text=proxy.var)))
                    ll.w[proxyvar==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==1,]),log=TRUE)
                    ll.w[proxyvar==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==0,]),log=TRUE,lower.tail=FALSE)
                }

                ## probability of the coded variables
                coder.lls <- matrix(nrow=nrow(df.temp),ncol=length(coder_formulas))
                ci <- 1
                for(coder_formula in coder_formulas){
                    coder.model.matrix <- model.matrix(coder_formula, df.temp)
                    n.coder.model.covars <- dim(coder.model.matrix)[2]
                    coder.params <- params[param.idx:(n.coder.model.covars + param.idx - 1)]
                    param.idx <- param.idx + n.coder.model.covars
                    coder.var <- all.vars(coder_formula)[1]
                    x.obs <- with(df.temp, eval(parse(text=coder.var)))
                    true.codervar <- df[[all.vars(coder_formula)[1]]]

                    ll.coder <- vector(mode='numeric', length=dim(coder.model.matrix)[1])
                    ll.coder[x.obs==1] <- plogis(coder.params %*% t(coder.model.matrix[x.obs==1,]),log=TRUE)
                    ll.coder[x.obs==0] <- plogis(coder.params %*% t(coder.model.matrix[x.obs==0,]),log=TRUE,lower.tail=FALSE)

                    # don't count when we know the observed value, unless we're accounting for observed value
                    ll.coder[(!is.na(true.codervar)) & (true.codervar != x.obs)] <- NA
                    coder.lls[,ci] <- ll.coder
                    ci <- ci + 1
                }
                
                truth.model.matrix <- model.matrix(truth_formula, df.temp)
                n.truth.model.covars <- dim(truth.model.matrix)[2]
                truth.params <- params[param.idx:(n.truth.model.covars + param.idx - 1)]

                for(coder_formula in coder_formulas){
                    coder.model.matrix <- model.matrix(coder_formula, df.temp)
                    n.coder.model.covars <- dim(coder.model.matrix)[2]
                    param.idx <- param.idx - n.coder.model.covars
                }

                x <- with(df.temp, eval(parse(text=truth.var)))
                ll.truth <- vector(mode='numeric', length=dim(truth.model.matrix)[1])
                ll.truth[x==1] <- plogis(truth.params %*% t(truth.model.matrix[x==1,]), log=TRUE)
                ll.truth[x==0] <- plogis(truth.params %*% t(truth.model.matrix[x==0,]), log=TRUE, lower.tail=FALSE)

                true.truthvar <- df[[all.vars(truth_formula)[1]]]
                
                if(!is.null(true.truthvar)){
                                        # ll.truth[(!is.na(true.truthvar)) & (true.truthvar != truthvar)] <- -Inf
                    # ll.truth[(!is.na(true.truthvar)) & (true.truthvar == truthvar)] <- 0
                }
                ll.parts[,i] <- ll.y + ll.w + apply(coder.lls,1,sum) + ll.truth
                
            }

            lls <- rowLogSumExps(ll.parts,na.rm=TRUE)

        ## likelihood of observed data 
            target <- -1 * sum(lls)
            return(target)
        }
    }
        
    outcome.params <- colnames(model.matrix(outcome_formula,df))
    lower <- rep(-Inf, length(outcome.params))

    if(outcome_family$family=='gaussian'){
        params <- c(outcome.params, 'sigma_y')
        lower <- c(lower, 0.00001)
    } else {
        params <- outcome.params
    }

    proxy.params <- colnames(model.matrix(proxy_formula, df))
    params <- c(params, paste0('proxy_',proxy.params))
    positive.params <- paste0('proxy_',truth.var)
    lower <- c(lower, rep(-Inf, length(proxy.params)))
    names(lower) <- params
    lower[positive.params] <- 0.01
    ci <- 0
    
    for(coder_formula in coder_formulas){
        coder.params <- colnames(model.matrix(coder_formula,df))
        params <- c(params, paste0('coder_',ci,coder.params))
        positive.params <- paste0('coder_', ci, truth.var)
        ci <- ci + 1
        lower <- c(lower, rep(-Inf, length(coder.params)))
        names(lower) <- params
        lower[positive.params] <- 0.01
    }

    truth.params <- colnames(model.matrix(truth_formula, df))
    params <- c(params, paste0('truth_', truth.params))
    lower <- c(lower, rep(-Inf, length(truth.params)))
    start <- rep(0.1,length(params))
    names(start) <- params
    names(lower) <- params
    
    if(method=='optim'){
        print(start)
        fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
    } else {
                
        quoted.names <- gsub("[\\(\\)]",'',names(start))
        print(quoted.names)
        text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(nll(params))}")

        measerr_mle_nll <- eval(parse(text=text))
        names(start) <- quoted.names
        names(lower) <- quoted.names
        fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, method='L-BFGS-B',control=list(maxit=1e6))
    }

    return(fit)
}

## Experimental, and does not work.
measerr_irr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='logit'), coder_formulas=list(y.obs.0~y+w_pred+y.obs.1,y.obs.1~y+w_pred+y.obs.0), proxy_formula=w_pred~y, proxy_family=binomial(link='logit'),method='optim'){
    integrate.grid <- expand.grid(replicate(1 + length(coder_formulas), c(0,1), simplify=FALSE))
    print(integrate.grid)


    outcome.model.matrix <- model.matrix(outcome_formula, df)
    n.outcome.model.covars <- dim(outcome.model.matrix)[2]


    ### in this scenario, the ground truth also has measurement error, but we have repeated measures for it. 
    # this time we never get to observe the true X
    nll <- function(params){
        param.idx <- 1
        outcome.params <- params[param.idx:n.outcome.model.covars]
        param.idx <- param.idx + n.outcome.model.covars
        proxy.model.matrix <- model.matrix(proxy_formula, df)
        n.proxy.model.covars <- dim(proxy.model.matrix)[2]
        response.var <- all.vars(outcome_formula)[1]

        if(outcome_family$family == "gaussian"){
            sigma.y <- params[param.idx]
            param.idx <- param.idx + 1
        }

        proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
        param.idx <- param.idx + n.proxy.model.covars

        df.temp <- copy(df)

        if((outcome_family$family == "binomial")
           & (outcome_family$link=='logit')){
            ll.parts <- matrix(nrow=nrow(df),ncol=nrow(integrate.grid))
            for(i in 1:nrow(integrate.grid)){
                # setup the dataframe for this row
                row <- integrate.grid[i,]

                df.temp[[response.var]] <- row[[1]]
                ci <- 2
                for(coder_formula in coder_formulas){
                    codervar <- all.vars(coder_formula)[1]
                    df.temp[[codervar]] <- row[[ci]]
                    ci <- ci + 1 
                }
                
                outcome.model.matrix <- model.matrix(outcome_formula, df.temp)                
                if(outcome_family$family == "gaussian"){
                    ll.y <- dnorm(df.temp[[response.var]], outcome.params %*% t(outcome.model.matrix), sd=sigma.y, log=T)
                }

                if(outcome_family$family == "binomial" & (outcome_family$link=='logit')){
                    ll.y <- vector(mode='numeric',length=nrow(df.temp))
                    ll.y[df.temp[[response.var]]==1] <- plogis( outcome.params %*% t(outcome.model.matrix), log=TRUE)
                    ll.y[df.temp[[response.var]]==0] <- plogis( outcome.params %*% t(outcome.model.matrix), log=TRUE,lower.tail=FALSE)
                }

                if(proxy_family$family=="binomial" & (proxy_family$link=='logit')){
                    proxy.model.matrix <- model.matrix(proxy_formula, df.temp)
                    ll.w <- vector(mode='numeric', length=dim(proxy.model.matrix)[1])
                    proxyvar <- with(df.temp,eval(parse(text=all.vars(proxy_formula)[1])))
                    ll.w[proxyvar==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==1,]),log=TRUE)
                    ll.w[proxyvar==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==0,]),log=TRUE,lower.tail=FALSE)
                }

                ## probability of the coded variables
                coder.lls <- matrix(nrow=nrow(df.temp),ncol=length(coder_formulas))
                ci <- 1
                for(coder_formula in coder_formulas){
                    coder.model.matrix <- model.matrix(coder_formula, df.temp)
                    n.coder.model.covars <- dim(coder.model.matrix)[2]
                    coder.params <- params[param.idx:(n.coder.model.covars + param.idx - 1)]
                    param.idx <- param.idx + n.coder.model.covars
                    codervar <- with(df.temp, eval(parse(text=all.vars(coder_formula)[1])))
                    true.codervar <- df[[all.vars(coder_formula)[1]]]

                    ll.coder <- vector(mode='numeric', length=dim(coder.model.matrix)[1])
                    ll.coder[codervar==1] <- plogis(coder.params %*% t(coder.model.matrix[codervar==1,]),log=TRUE)
                    ll.coder[codervar==0] <- plogis(coder.params %*% t(coder.model.matrix[codervar==0,]),log=TRUE,lower.tail=FALSE)

                    # don't count when we know the observed value, unless we're accounting for observed value
                    ll.coder[(!is.na(true.codervar)) & (true.codervar != codervar)] <- NA
                    coder.lls[,ci] <- ll.coder
                    ci <- ci + 1
                }

                for(coder_formula in coder_formulas){
                    coder.model.matrix <- model.matrix(coder_formula, df.temp)
                    n.coder.model.covars <- dim(coder.model.matrix)[2]
                    param.idx <- param.idx - n.coder.model.covars
                }

                ll.parts[,i] <- ll.y + ll.w + apply(coder.lls,1,function(x) sum(x)) 
                
            }

            lls <- rowLogSumExps(ll.parts,na.rm=TRUE)

            ## likelihood of observed data 
            target <- -1 * sum(lls)
            print(target)
            print(params)
            return(target)
        }
    }
        
    outcome.params <- colnames(model.matrix(outcome_formula,df))
    response.var <- all.vars(outcome_formula)[1]
    lower <- rep(-Inf, length(outcome.params))

    if(outcome_family$family=='gaussian'){
        params <- c(outcome.params, 'sigma_y')
        lower <- c(lower, 0.00001)
    } else {
        params <- outcome.params
    }

    ## constrain the model of the coder and proxy vars
    ## this is to ensure identifiability
    ## it is a safe assumption because the coders aren't hostile (wrong more often than right)
    ## so we can assume that y ~Bw, B is positive
    proxy.params <- colnames(model.matrix(proxy_formula, df))
    positive.params <- paste0('proxy_',response.var)
    params <- c(params, paste0('proxy_',proxy.params))
    lower <- c(lower, rep(-Inf, length(proxy.params)))
    names(lower) <- params
    lower[positive.params] <- 0.001

    ci <- 0
    for(coder_formula in coder_formulas){
        coder.params <- colnames(model.matrix(coder_formula,df))
        latent.coder.params <- coder.params %in% response.var
        params <- c(params, paste0('coder_',ci,coder.params))
        positive.params <- paste0('coder_',ci,response.var)
        ci <- ci + 1
        lower <- c(lower, rep(-Inf, length(coder.params)))
        names(lower) <-params
        lower[positive.params] <- 0.001
    }

    ## init by using the "loco model"
    temp.df <- copy(df)
    temp.df <- temp.df[y.obs.1 == y.obs.0, y:=y.obs.1]
    loco.model <- glm(outcome_formula, temp.df, family=outcome_family)
    
    start <- rep(1,length(params))
    names(start) <- params
    start[names(coef(loco.model))] <- coef(loco.model)
    names(lower) <- params
    if(method=='optim'){
        print(lower)
        fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE,control=list(maxit=1e6))
    } else {
                
        quoted.names <- gsub("[\\(\\)]",'',names(start))
        print(quoted.names)
        text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(nll(params))}")

        measerr_mle_nll <- eval(parse(text=text))
        names(start) <- quoted.names
        names(lower) <- quoted.names
        fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
    }

    return(fit)
}