228 lines
11 KiB
R
228 lines
11 KiB
R
library(formula.tools)
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library(matrixStats)
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## df: dataframe to model
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## outcome_formula: formula for y | x, z
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## outcome_family: family for y | x, z
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## proxy_formula: formula for w | x, z, y
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## proxy_family: family for w | x, z, y
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## truth_formula: formula for x | z
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## truth_family: family for x | z
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### ideal formulas for example 1
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# test.fit.1 <- measerr_mle(df, y ~ x + z, gaussian(), w_pred ~ x, binomial(link='logit'), x ~ z)
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### ideal formulas for example 2
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# test.fit.2 <- measerr_mle(df, y ~ x + z, gaussian(), w_pred ~ x + z + y + y:x, binomial(link='logit'), x ~ z)
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## outcome_formula <- y ~ x + z; proxy_formula <- w_pred ~ y + x + z + x:z + x:y + z:y
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measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='logit'), proxy_formula, proxy_family=binomial(link='logit')){
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nll <- function(params){
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df.obs <- model.frame(outcome_formula, df)
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proxy.variable <- all.vars(proxy_formula)[1]
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proxy.model.matrix <- model.matrix(proxy_formula, df)
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response.var <- all.vars(outcome_formula)[1]
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y.obs <- with(df.obs,eval(parse(text=response.var)))
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outcome.model.matrix <- model.matrix(outcome_formula, df.obs)
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param.idx <- 1
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n.outcome.model.covars <- dim(outcome.model.matrix)[2]
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outcome.params <- params[param.idx:n.outcome.model.covars]
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param.idx <- param.idx + n.outcome.model.covars
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if((outcome_family$family == "binomial") & (outcome_family$link == 'logit')){
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ll.y.obs <- vector(mode='numeric', length=length(y.obs))
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ll.y.obs[y.obs==1] <- plogis(outcome.params %*% t(outcome.model.matrix[y.obs==1,]),log=TRUE)
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ll.y.obs[y.obs==0] <- plogis(outcome.params %*% t(outcome.model.matrix[y.obs==0,]),log=TRUE,lower.tail=FALSE)
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}
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df.obs <- model.frame(proxy_formula,df)
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n.proxy.model.covars <- dim(proxy.model.matrix)[2]
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proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
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param.idx <- param.idx + n.proxy.model.covars
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proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))
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if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
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ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
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ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
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ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
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}
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ll.obs <- sum(ll.y.obs + ll.w.obs)
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df.unobs <- df[is.na(df[[response.var]])]
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df.unobs.y1 <- copy(df.unobs)
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df.unobs.y1[[response.var]] <- 1
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df.unobs.y0 <- copy(df.unobs)
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df.unobs.y0[[response.var]] <- 1
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## integrate out y
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outcome.model.matrix.y1 <- model.matrix(outcome_formula, df.unobs.y1)
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if((outcome_family$family == "binomial") & (outcome_family$link == 'logit')){
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ll.y.unobs.1 <- vector(mode='numeric', length=dim(outcome.model.matrix.y1)[1])
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ll.y.unobs.0 <- vector(mode='numeric', length=dim(outcome.model.matrix.y1)[1])
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ll.y.unobs.1 <- plogis(outcome.params %*% t(outcome.model.matrix.y1),log=TRUE)
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ll.y.unobs.0 <- plogis(outcome.params %*% t(outcome.model.matrix.y1),log=TRUE,lower.tail=FALSE)
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}
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proxy.model.matrix.y1 <- model.matrix(proxy_formula, df.unobs.y1)
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proxy.model.matrix.y0 <- model.matrix(proxy_formula, df.unobs.y0)
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proxy.unobs <- with(df.unobs, eval(parse(text=proxy.variable)))
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if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
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ll.w.unobs.1 <- vector(mode='numeric',length=dim(proxy.model.matrix.y1)[1])
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ll.w.unobs.0 <- vector(mode='numeric',length=dim(proxy.model.matrix.y0)[1])
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ll.w.unobs.1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.y1[proxy.unobs==1,]),log=TRUE)
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ll.w.unobs.1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.y1[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
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ll.w.unobs.0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.y0[proxy.unobs==1,]),log=TRUE)
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ll.w.unobs.0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.y0[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
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}
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ll.unobs.1 <- ll.y.unobs.1 + ll.w.unobs.1
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ll.unobs.0 <- ll.y.unobs.0 + ll.w.unobs.0
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ll.unobs <- sum(colLogSumExps(rbind(ll.unobs.1,ll.unobs.0)))
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ll <- ll.unobs + ll.obs
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return(-ll)
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}
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params <- colnames(model.matrix(outcome_formula,df))
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lower <- rep(-Inf, length(params))
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proxy.params <- colnames(model.matrix(proxy_formula, df))
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params <- c(params, paste0('proxy_',proxy.params))
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lower <- c(lower, rep(-Inf, length(proxy.params)))
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start <- rep(0.1,length(params))
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names(start) <- params
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fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
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return(fit)
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}
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measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit')){
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measrr_mle_nll <- function(params){
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df.obs <- model.frame(outcome_formula, df)
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proxy.variable <- all.vars(proxy_formula)[1]
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proxy.model.matrix <- model.matrix(proxy_formula, df)
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response.var <- all.vars(outcome_formula)[1]
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y.obs <- with(df.obs,eval(parse(text=response.var)))
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outcome.model.matrix <- model.matrix(outcome_formula, df)
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param.idx <- 1
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n.outcome.model.covars <- dim(outcome.model.matrix)[2]
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outcome.params <- params[param.idx:n.outcome.model.covars]
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param.idx <- param.idx + n.outcome.model.covars
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## likelihood for the fully observed data
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if(outcome_family$family == "gaussian"){
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sigma.y <- params[param.idx]
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param.idx <- param.idx + 1
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ll.y.obs <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix),sd=sigma.y, log=TRUE)
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}
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df.obs <- model.frame(proxy_formula,df)
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n.proxy.model.covars <- dim(proxy.model.matrix)[2]
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proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
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param.idx <- param.idx + n.proxy.model.covars
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proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))
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if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
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ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
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ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
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ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
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}
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df.obs <- model.frame(truth_formula, df)
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truth.variable <- all.vars(truth_formula)[1]
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truth.obs <- with(df.obs, eval(parse(text=truth.variable)))
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truth.model.matrix <- model.matrix(truth_formula,df)
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n.truth.model.covars <- dim(truth.model.matrix)[2]
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truth.params <- params[param.idx:(n.truth.model.covars + param.idx - 1)]
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if( (truth_family$family=="binomial") & (truth_family$link=='logit')){
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ll.x.obs <- vector(mode='numeric',length=dim(truth.model.matrix)[1])
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ll.x.obs[truth.obs==1] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==1,]),log=TRUE)
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ll.x.obs[truth.obs==0] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==0,]),log=TRUE, lower.tail=FALSE)
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}
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ll.obs <- sum(ll.y.obs + ll.w.obs + ll.x.obs)
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## likelihood for the predicted data
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## integrate out the "truth" variable.
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if(truth_family$family=='binomial'){
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df.unobs <- df[is.na(eval(parse(text=truth.variable)))]
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df.unobs.x1 <- copy(df.unobs)
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df.unobs.x1[,'x'] <- 1
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df.unobs.x0 <- copy(df.unobs)
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df.unobs.x0[,'x'] <- 0
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outcome.unobs <- with(df.unobs, eval(parse(text=response.var)))
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outcome.model.matrix.x0 <- model.matrix(outcome_formula, df.unobs.x0)
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outcome.model.matrix.x1 <- model.matrix(outcome_formula, df.unobs.x1)
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if(outcome_family$family=="gaussian"){
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ll.y.x0 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x0), sd=sigma.y, log=TRUE)
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ll.y.x1 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x1), sd=sigma.y, log=TRUE)
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}
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if( (proxy_family$family=='binomial') & (proxy_family$link=='logit')){
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proxy.model.matrix.x0 <- model.matrix(proxy_formula, df.unobs.x0)
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proxy.model.matrix.x1 <- model.matrix(proxy_formula, df.unobs.x1)
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proxy.unobs <- df.unobs[[proxy.variable]]
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ll.w.x0 <- vector(mode='numeric', length=dim(df.unobs)[1])
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ll.w.x1 <- vector(mode='numeric', length=dim(df.unobs)[1])
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ll.w.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==1,]), log=TRUE)
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ll.w.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==1,]), log=TRUE)
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ll.w.x0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
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ll.w.x1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
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}
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if(truth_family$link=='logit'){
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truth.model.matrix <- model.matrix(truth_formula, df.unobs.x0)
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ll.x.x0 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE)
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ll.x.x1 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE, lower.tail=FALSE)
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}
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}
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ll.x0 <- ll.y.x0 + ll.w.x0 + ll.x.x0
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ll.x1 <- ll.y.x1 + ll.w.x1 + ll.x.x1
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ll.unobs <- sum(colLogSumExps(rbind(ll.x0, ll.x1)))
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return(-(ll.unobs + ll.obs))
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}
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outcome.params <- colnames(model.matrix(outcome_formula,df))
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lower <- rep(-Inf, length(outcome.params))
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if(outcome_family$family=='gaussian'){
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params <- c(outcome.params, 'sigma_y')
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lower <- c(lower, 0.00001)
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} else {
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params <- outcome.params
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}
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proxy.params <- colnames(model.matrix(proxy_formula, df))
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params <- c(params, paste0('proxy_',proxy.params))
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lower <- c(lower, rep(-Inf, length(proxy.params)))
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truth.params <- colnames(model.matrix(truth_formula, df))
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params <- c(params, paste0('truth_', truth.params))
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lower <- c(lower, rep(-Inf, length(truth.params)))
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start <- rep(0.1,length(params))
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names(start) <- params
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fit <- optim(start, fn = measrr_mle_nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
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return(fit)
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}
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