library(formula.tools)
library(matrixStats)
-
+library(bbmle)
## df: dataframe to model
## outcome_formula: formula for y | x, z
## outcome_family: family for y | 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')){
+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)
df.unobs.y1 <- copy(df.unobs)
df.unobs.y1[[response.var]] <- 1
df.unobs.y0 <- copy(df.unobs)
- df.unobs.y0[[response.var]] <- 1
+ df.unobs.y0[[response.var]] <- 0
## integrate out y
outcome.model.matrix.y1 <- model.matrix(outcome_formula, df.unobs.y1)
start <- rep(0.1,length(params))
names(start) <- params
- fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
+ 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')){
+## Experimental, and not necessary if errors are independent.
+measerr_irr_mle <- function(df, outcome_formula, outcome_family=gaussian(), rater_formula, proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit'),method='optim'){
- measrr_mle_nll <- function(params){
- df.obs <- model.frame(outcome_formula, df)
+ ### in this scenario, the ground truth also has measurement error, but we have repeated measures for it.
+
+ ## probability of y given observed data.
+ df.obs <- df[!is.na(x.obs.1)]
+ proxy.variable <- all.vars(proxy_formula)[1]
+ df.x.obs.1 <- copy(df.obs)[,x:=1]
+ df.x.obs.0 <- copy(df.obs)[,x:=0]
+ y.obs <- df.obs[,y]
+
+ nll <- function(params){
+ outcome.model.matrix.x.obs.0 <- model.matrix(outcome_formula, df.x.obs.0)
+ outcome.model.matrix.x.obs.1 <- model.matrix(outcome_formula, df.x.obs.1)
+
+ param.idx <- 1
+ n.outcome.model.covars <- dim(outcome.model.matrix.x.obs.0)[2]
+ outcome.params <- params[param.idx:n.outcome.model.covars]
+ param.idx <- param.idx + n.outcome.model.covars
+
+ sigma.y <- params[param.idx]
+ param.idx <- param.idx + 1
+
+ ll.y.x.obs.0 <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix.x.obs.0),sd=sigma.y, log=TRUE)
+ ll.y.x.obs.1 <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix.x.obs.1),sd=sigma.y, log=TRUE)
+
+ ## assume that the two coders are statistically independent conditional on x
+ ll.x.obs.0.x0 <- vector(mode='numeric', length=nrow(df.obs))
+ ll.x.obs.1.x0 <- vector(mode='numeric', length=nrow(df.obs))
+ ll.x.obs.0.x1 <- vector(mode='numeric', length=nrow(df.obs))
+ ll.x.obs.1.x1 <- vector(mode='numeric', length=nrow(df.obs))
+
+ rater.model.matrix.x.obs.0 <- model.matrix(rater_formula, df.x.obs.0)
+ rater.model.matrix.x.obs.1 <- model.matrix(rater_formula, df.x.obs.1)
+
+ n.rater.model.covars <- dim(rater.model.matrix.x.obs.0)[2]
+ rater.0.params <- params[param.idx:(n.rater.model.covars + param.idx - 1)]
+ param.idx <- param.idx + n.rater.model.covars
+
+ rater.1.params <- params[param.idx:(n.rater.model.covars + param.idx - 1)]
+ param.idx <- param.idx + n.rater.model.covars
+
+ # probability of rater 0 if x is 0 or 1
+ ll.x.obs.0.x0[df.obs$x.obs.0==1] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.0==1,]), log=TRUE)
+ ll.x.obs.0.x0[df.obs$x.obs.0==0] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.0==0,]), log=TRUE, lower.tail=FALSE)
+ ll.x.obs.0.x1[df.obs$x.obs.0==1] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.0==1,]), log=TRUE)
+ ll.x.obs.0.x1[df.obs$x.obs.0==0] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.0==0,]), log=TRUE, lower.tail=FALSE)
+
+ # probability of rater 1 if x is 0 or 1
+ ll.x.obs.1.x0[df.obs$x.obs.1==1] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.1==1,]), log=TRUE)
+ ll.x.obs.1.x0[df.obs$x.obs.1==0] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.1==0,]), log=TRUE, lower.tail=FALSE)
+ ll.x.obs.1.x1[df.obs$x.obs.1==1] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.1==1,]), log=TRUE)
+ ll.x.obs.1.x1[df.obs$x.obs.1==0] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.1==0,]), log=TRUE, lower.tail=FALSE)
+
+ proxy.model.matrix.x0 <- model.matrix(proxy_formula, df.x.obs.0)
+ proxy.model.matrix.x1 <- model.matrix(proxy_formula, df.x.obs.1)
+
+ n.proxy.model.covars <- dim(proxy.model.matrix.x0)[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.x0 <- vector(mode='numeric',length=dim(proxy.model.matrix.x0)[1])
+ ll.w.obs.x1 <- vector(mode='numeric',length=dim(proxy.model.matrix.x1)[1])
+
+ # proxy_formula likelihood using logistic regression
+ ll.w.obs.x0[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.obs==1,]),log=TRUE)
+ ll.w.obs.x0[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
+
+ ll.w.obs.x1[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.obs==1,]),log=TRUE)
+ ll.w.obs.x1[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
+ }
+
+ ## assume that the probability of x is a logistic regression depending on z
+ truth.model.matrix.obs <- model.matrix(truth_formula, df.obs)
+ n.truth.params <- dim(truth.model.matrix.obs)[2]
+ truth.params <- params[param.idx:(n.truth.params + param.idx - 1)]
+
+ ll.obs.x0 <- plogis(truth.params %*% t(truth.model.matrix.obs), log=TRUE)
+ ll.obs.x1 <- plogis(truth.params %*% t(truth.model.matrix.obs), log=TRUE, lower.tail=FALSE)
+
+ ll.obs <- colLogSumExps(rbind(ll.y.x.obs.0 + ll.x.obs.0.x0 + ll.x.obs.1.x0 + ll.obs.x0 + ll.w.obs.x0,
+ ll.y.x.obs.1 + ll.x.obs.0.x1 + ll.x.obs.1.x1 + ll.obs.x1 + ll.w.obs.x1))
+
+ ### NOW FOR THE FUN PART. Likelihood of the unobserved data.
+ ### we have to integrate out x.obs.0, x.obs.1, and x.
+
+
+ ## THE OUTCOME
+ df.unobs <- df[is.na(x.obs)]
+ df.x.unobs.0 <- copy(df.unobs)[,x:=0]
+ df.x.unobs.1 <- copy(df.unobs)[,x:=1]
+ y.unobs <- df.unobs$y
+
+ outcome.model.matrix.x.unobs.0 <- model.matrix(outcome_formula, df.x.unobs.0)
+ outcome.model.matrix.x.unobs.1 <- model.matrix(outcome_formula, df.x.unobs.1)
+
+ ll.y.unobs.x0 <- dnorm(y.unobs, outcome.params %*% t(outcome.model.matrix.x.unobs.0), sd=sigma.y, log=TRUE)
+ ll.y.unobs.x1 <- dnorm(y.unobs, outcome.params %*% t(outcome.model.matrix.x.unobs.1), sd=sigma.y, log=TRUE)
+
+
+ ## THE UNLABELED DATA
+
+
+ ## assume that the two coders are statistically independent conditional on x
+ ll.x.unobs.0.x0 <- vector(mode='numeric', length=nrow(df.unobs))
+ ll.x.unobs.1.x0 <- vector(mode='numeric', length=nrow(df.unobs))
+ ll.x.unobs.0.x1 <- vector(mode='numeric', length=nrow(df.unobs))
+ ll.x.unobs.1.x1 <- vector(mode='numeric', length=nrow(df.unobs))
+ df.x.unobs.0[,x.obs := 1]
+ df.x.unobs.1[,x.obs := 1]
+
+ rater.model.matrix.x.unobs.0 <- model.matrix(rater_formula, df.x.unobs.0)
+ rater.model.matrix.x.unobs.1 <- model.matrix(rater_formula, df.x.unobs.1)
+
+
+ ## # probability of rater 0 if x is 0 or 1
+ ## ll.x.unobs.0.x0 <- colLogSumExps(rbind(plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE),
+ ## plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE, lower.tail=TRUE)))
+
+ ## ll.x.unobs.0.x1 <- colLogSumExps(rbind(plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE),
+ ## plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE, lower.tail=TRUE)))
+
+ ## # probability of rater 1 if x is 0 or 1
+ ## ll.x.unobs.1.x0 <- colLogSumExps(rbind(plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE),
+ ## plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE, lower.tail=TRUE)))
+
+ ## ll.x.unobs.1.x1 <- colLogSumExps(rbind(plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE),
+ ## plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE, lower.tail=TRUE)))
+
+
+ proxy.unobs <- with(df.unobs, eval(parse(text=proxy.variable)))
+ proxy.model.matrix.x0.unobs <- model.matrix(proxy_formula, df.x.unobs.0)
+ proxy.model.matrix.x1.unobs <- model.matrix(proxy_formula, df.x.unobs.1)
+
+ if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
+ ll.w.unobs.x0 <- vector(mode='numeric',length=dim(proxy.model.matrix.x0)[1])
+ ll.w.unobs.x1 <- vector(mode='numeric',length=dim(proxy.model.matrix.x1)[1])
+
+
+ # proxy_formula likelihood using logistic regression
+ ll.w.unobs.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0.unobs[proxy.unobs==1,]),log=TRUE)
+ ll.w.unobs.x0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0.unobs[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
+
+ ll.w.unobs.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1.unobs[proxy.unobs==1,]),log=TRUE)
+ ll.w.unobs.x1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1.unobs[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
+ }
+
+ truth.model.matrix.unobs <- model.matrix(truth_formula, df.unobs)
+
+ ll.unobs.x0 <- plogis(truth.params %*% t(truth.model.matrix.unobs), log=TRUE)
+ ll.unobs.x1 <- plogis(truth.params %*% t(truth.model.matrix.unobs), log=TRUE, lower.tail=FALSE)
+
+ ll.unobs <- colLogSumExps(rbind(ll.unobs.x0 + ll.w.unobs.x0 + ll.y.unobs.x0,
+ ll.unobs.x1 + ll.w.unobs.x1 + ll.y.unobs.x1))
+
+ return(-1 *( sum(ll.obs) + sum(ll.unobs)))
+ }
+
+ outcome.params <- colnames(model.matrix(outcome_formula,df))
+ lower <- rep(-Inf, length(outcome.params))
+
+ if(outcome_family$family=='gaussian'){
+ params <- c(outcome.params, 'sigma_y')
+ lower <- c(lower, 0.00001)
+ } else {
+ params <- outcome.params
+ }
+
+ rater.0.params <- colnames(model.matrix(rater_formula,df))
+ params <- c(params, paste0('rater_0',rater.0.params))
+ lower <- c(lower, rep(-Inf, length(rater.0.params)))
+
+ rater.1.params <- colnames(model.matrix(rater_formula,df))
+ params <- c(params, paste0('rater_1',rater.1.params))
+ lower <- c(lower, rep(-Inf, length(rater.1.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 = 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'){
+
+ measerr_mle_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)
param.idx <- 1
if(outcome_family$family == "gaussian"){
sigma.y <- params[param.idx]
param.idx <- param.idx + 1
+
+ # outcome_formula likelihood using linear regression
ll.y.obs <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix),sd=sigma.y, log=TRUE)
}
if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
+
+ # proxy_formula likelihood using logistic regression
ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
}
if( (truth_family$family=="binomial") & (truth_family$link=='logit')){
ll.x.obs <- vector(mode='numeric',length=dim(truth.model.matrix)[1])
+
+ # truth_formula likelihood using logistic regression
ll.x.obs[truth.obs==1] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==1,]),log=TRUE)
ll.x.obs[truth.obs==0] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==0,]),log=TRUE, lower.tail=FALSE)
}
+ # add the three likelihoods
ll.obs <- sum(ll.y.obs + ll.w.obs + ll.x.obs)
## likelihood for the predicted data
outcome.model.matrix.x0 <- model.matrix(outcome_formula, df.unobs.x0)
outcome.model.matrix.x1 <- model.matrix(outcome_formula, df.unobs.x1)
if(outcome_family$family=="gaussian"){
- 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)
+
+ # 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')){
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)
if(truth_family$link=='logit'){
truth.model.matrix <- model.matrix(truth_formula, df.unobs.x0)
- ll.x.x0 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE)
- ll.x.x1 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE, lower.tail=FALSE)
+ # 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)
}
}
lower <- c(lower, rep(-Inf, length(truth.params)))
start <- rep(0.1,length(params))
names(start) <- params
-
- fit <- optim(start, fn = measrr_mle_nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
+
+ 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)
}
+
projects / ml_measurement_error_public.git / blobdiff