598 lines
27 KiB
R
598 lines
27 KiB
R
library(formula.tools)
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library(matrixStats)
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library(optimx)
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library(bbmle)
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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'),method='optim'){
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df.obs <- model.frame(outcome_formula, df)
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proxy.model.matrix <- model.matrix(proxy_formula, df)
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proxy.variable <- all.vars(proxy_formula)[1]
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df.proxy.obs <- model.frame(proxy_formula,df)
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proxy.obs <- with(df.proxy.obs, eval(parse(text=proxy.variable)))
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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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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]] <- 0
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outcome.model.matrix.y1 <- model.matrix(outcome_formula, df.unobs.y1)
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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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nll <- function(params){
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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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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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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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## integrate out y
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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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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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if(method=='optim'){
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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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} else {
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quoted.names <- gsub("[\\(\\)]",'',names(start))
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print(quoted.names)
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text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(nll(params))}")
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measerr_mle_nll <- eval(parse(text=text))
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names(start) <- quoted.names
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names(lower) <- quoted.names
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fit <- mle2(minuslogl=measerr_mle_nll, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
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}
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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'),method='optim'){
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df.obs <- model.frame(outcome_formula, df)
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response.var <- all.vars(outcome_formula)[1]
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proxy.variable <- all.vars(proxy_formula)[1]
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truth.variable <- all.vars(truth_formula)[1]
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outcome.model.matrix <- model.matrix(outcome_formula, df)
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proxy.model.matrix <- model.matrix(proxy_formula, df)
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y.obs <- with(df.obs,eval(parse(text=response.var)))
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measerr_mle_nll <- function(params){
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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$family == "gaussian"){
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sigma.y <- params[param.idx]
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param.idx <- param.idx + 1
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# outcome_formula likelihood using linear regression
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ll.y.obs <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix),sd=sigma.y, log=TRUE)
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}
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df.obs <- model.frame(proxy_formula,df)
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n.proxy.model.covars <- dim(proxy.model.matrix)[2]
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proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
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param.idx <- param.idx + n.proxy.model.covars
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proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))
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if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
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ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
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# proxy_formula likelihood using logistic regression
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ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
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ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
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}
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df.obs <- model.frame(truth_formula, df)
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truth.obs <- with(df.obs, eval(parse(text=truth.variable)))
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truth.model.matrix <- model.matrix(truth_formula,df)
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n.truth.model.covars <- dim(truth.model.matrix)[2]
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truth.params <- params[param.idx:(n.truth.model.covars + param.idx - 1)]
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if( (truth_family$family=="binomial") & (truth_family$link=='logit')){
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ll.x.obs <- vector(mode='numeric',length=dim(truth.model.matrix)[1])
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# truth_formula likelihood using logistic regression
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ll.x.obs[truth.obs==1] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==1,]),log=TRUE)
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ll.x.obs[truth.obs==0] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==0,]),log=TRUE, lower.tail=FALSE)
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}
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# add the three likelihoods
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ll.obs <- sum(ll.y.obs + ll.w.obs + ll.x.obs)
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## likelihood for the predicted data
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## integrate out the "truth" variable.
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if(truth_family$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$family=="gaussian"){
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# likelihood of outcome
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ll.y.x0 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x0), sd=sigma.y, log=TRUE)
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ll.y.x1 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x1), sd=sigma.y, log=TRUE)
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}
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if( (proxy_family$family=='binomial') & (proxy_family$link=='logit')){
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proxy.model.matrix.x0 <- model.matrix(proxy_formula, df.unobs.x0)
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proxy.model.matrix.x1 <- model.matrix(proxy_formula, df.unobs.x1)
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proxy.unobs <- df.unobs[[proxy.variable]]
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ll.w.x0 <- vector(mode='numeric', length=dim(df.unobs)[1])
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ll.w.x1 <- vector(mode='numeric', length=dim(df.unobs)[1])
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# likelihood of proxy
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ll.w.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==1,]), log=TRUE)
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ll.w.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==1,]), log=TRUE)
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ll.w.x0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
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ll.w.x1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==0,]), log=TRUE,lower.tail=FALSE)
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}
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if(truth_family$link=='logit'){
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truth.model.matrix <- model.matrix(truth_formula, df.unobs.x0)
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# likelihood of truth
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ll.x.x1 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE)
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ll.x.x0 <- 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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if(method=='optim'){
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fit <- optim(start, fn = measerr_mle_nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
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} else { # method='mle2'
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quoted.names <- gsub("[\\(\\)]",'',names(start))
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text <- paste("function(", paste0(quoted.names,'=',start,collapse=','),"){params<-c(",paste0(quoted.names,collapse=','),");return(measerr_mle_nll(params))}")
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measerr_mle_nll_mle <- eval(parse(text=text))
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names(start) <- quoted.names
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names(lower) <- quoted.names
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fit <- mle2(minuslogl=measerr_mle_nll_mle, start=start, lower=lower, parnames=params,control=list(maxit=1e6),method='L-BFGS-B')
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}
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return(fit)
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}
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## Experimental, but probably works.
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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'){
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### in this scenario, the ground truth also has measurement error, but we have repeated measures for it.
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# this time we never get to observe the true X
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outcome.model.matrix <- model.matrix(outcome_formula, df)
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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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proxy.var <- all.vars(proxy_formula)[1]
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param.var <- all.vars(truth_formula)[1]
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truth.var<- all.vars(truth_formula)[1]
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y <- with(df,eval(parse(text=response.var)))
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nll <- function(params){
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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 == "gaussian"){
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sigma.y <- params[param.idx]
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param.idx <- param.idx + 1
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}
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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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df.temp <- copy(df)
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if((truth_family$family == "binomial")
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& (truth_family$link=='logit')){
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integrate.grid <- expand.grid(replicate(1 + length(coder_formulas), c(0,1), simplify=FALSE))
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ll.parts <- matrix(nrow=nrow(df),ncol=nrow(integrate.grid))
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for(i in 1:nrow(integrate.grid)){
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# setup the dataframe for this row
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row <- integrate.grid[i,]
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df.temp[[param.var]] <- row[[1]]
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ci <- 2
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for(coder_formula in coder_formulas){
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coder.var <- all.vars(coder_formula)[1]
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df.temp[[coder.var]] <- row[[ci]]
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ci <- ci + 1
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}
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outcome.model.matrix <- model.matrix(outcome_formula, df.temp)
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if(outcome_family$family == "gaussian"){
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ll.y <- dnorm(y, outcome.params %*% t(outcome.model.matrix), sd=sigma.y, log=TRUE)
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}
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if(proxy_family$family=="binomial" & (proxy_family$link=='logit')){
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proxy.model.matrix <- model.matrix(proxy_formula, df.temp)
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ll.w <- vector(mode='numeric', length=dim(proxy.model.matrix)[1])
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proxyvar <- with(df.temp,eval(parse(text=proxy.var)))
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ll.w[proxyvar==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==1,]),log=TRUE)
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ll.w[proxyvar==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxyvar==0,]),log=TRUE,lower.tail=FALSE)
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}
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## probability of the coded variables
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coder.lls <- matrix(nrow=nrow(df.temp),ncol=length(coder_formulas))
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ci <- 1
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for(coder_formula in coder_formulas){
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coder.model.matrix <- model.matrix(coder_formula, df.temp)
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n.coder.model.covars <- dim(coder.model.matrix)[2]
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coder.params <- params[param.idx:(n.coder.model.covars + param.idx - 1)]
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param.idx <- param.idx + n.coder.model.covars
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coder.var <- all.vars(coder_formula)[1]
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x.obs <- with(df.temp, eval(parse(text=coder.var)))
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true.codervar <- df[[all.vars(coder_formula)[1]]]
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ll.coder <- vector(mode='numeric', length=dim(coder.model.matrix)[1])
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ll.coder[x.obs==1] <- plogis(coder.params %*% t(coder.model.matrix[x.obs==1,]),log=TRUE)
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ll.coder[x.obs==0] <- plogis(coder.params %*% t(coder.model.matrix[x.obs==0,]),log=TRUE,lower.tail=FALSE)
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# don't count when we know the observed value, unless we're accounting for observed value
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ll.coder[(!is.na(true.codervar)) & (true.codervar != x.obs)] <- NA
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coder.lls[,ci] <- ll.coder
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ci <- ci + 1
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}
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truth.model.matrix <- model.matrix(truth_formula, df.temp)
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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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for(coder_formula in coder_formulas){
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coder.model.matrix <- model.matrix(coder_formula, df.temp)
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n.coder.model.covars <- dim(coder.model.matrix)[2]
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param.idx <- param.idx - n.coder.model.covars
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}
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x <- with(df.temp, eval(parse(text=truth.var)))
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ll.truth <- vector(mode='numeric', length=dim(truth.model.matrix)[1])
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ll.truth[x==1] <- plogis(truth.params %*% t(truth.model.matrix[x==1,]), log=TRUE)
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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)
|
|
}
|
|
|