From: Nathan TeBlunthuis Date: Fri, 1 Jul 2022 02:00:35 +0000 (-0700) Subject: add mle methods from carroll X-Git-Url: https://code.communitydata.science/ml_measurement_error_public.git/commitdiff_plain/588bdd7ed74cf8fe8fd0f15df58a6a40c26ebae5 add mle methods from carroll --- diff --git a/simulations/01_two_covariates.R b/simulations/01_two_covariates.R index 419403d..7b8e12e 100644 --- a/simulations/01_two_covariates.R +++ b/simulations/01_two_covariates.R @@ -50,8 +50,8 @@ simulate_data <- function(N, m, B0=0, Bxy=0.2, Bgy=-0.2, Bgx=0.2, y_explained_va } df <- df[,w_pred:=x] - df <- df[sample(1:N,(1-prediction_accuracy)*N),w_pred:=(w_pred-1)**2] + w <- predict(glm(x ~ w_pred,data=df,family=binomial(link='logit')),type='response') df <- df[,':='(w=w, w_pred = w_pred)] return(df) } @@ -61,15 +61,20 @@ parser <- add_argument(parser, "--N", default=500, help="number of observations parser <- add_argument(parser, "--m", default=100, help="m the number of ground truth observations") parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng') parser <- add_argument(parser, "--outfile", help='output file', default='example_1.feather') +parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005) +parser <- add_argument(parser, "--gx_explained_variance", help='what proportion of the variance of x can be explained by g?', default=0.15) +parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73) + args <- parse_args(parser) B0 <- 0 Bxy <- 0.2 Bgy <- -0.2 -Bgx <- 0.5 +Bgx <- 0.4 + +df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, Bgx, seed=args$seed, y_explained_variance = args$y_explained_variance, gx_explained_variance = args$gx_explained_variance, prediction_accuracy=args$prediction_accuracy) -df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, Bgx, seed=args$seed, y_explained_variance = 0.025, gx_explained_variance = 0.15) -result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bgx'=Bgx, 'seed'=args$seed) +result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bgx'=Bgx, 'seed'=args$seed, 'y_explained_variance' = args$y_explained_variance, 'gx_explained_variance' = args$gx_explained_variance, "prediction_accuracy"=args$prediction_accuracy) outline <- run_simulation(df, result) outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE) diff --git a/simulations/02_indep_differential.R b/simulations/02_indep_differential.R index 5a7784b..d4e0916 100644 --- a/simulations/02_indep_differential.R +++ b/simulations/02_indep_differential.R @@ -31,68 +31,70 @@ source("simulation_base.R") ## one way to do it is by adding correlation to x.obs and y that isn't in w. ## in other words, the model is missing an important feature of x.obs that's related to y. -simulate_data <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed, xy.explained.variance=0.01, u.explained.variance=0.1){ +simulate_data <- function(N, m, B0, Bxy, Bgy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){ set.seed(seed) - - ## the true value of x - - g <- rbinom(N, 1, 0.5) - # make w and y dependent - u <- rnorm(N,0,) - - xprime <- Bgx * g + rnorm(N,0,1) - - k <- Bkx*xprime + rnorm(N,0,1.5) + 1.1*Bkx*u - - x <- as.integer(logistic(scale(xprime)) > 0.5) - - y <- Bxy * x + Bgy * g + B0 + u + rnorm(N, 0, 1) + g <- rbinom(N, 1, 0.5) + x <- rbinom(N, 1, 0.5) - df <- data.table(x=x,k=k,y=y,g=g) + y.var.epsilon <- (var(Bgy * g) + var(Bxy *x) + 2*cov(Bgy*g,Bxy*x)) * ((1-y_explained_variance)/y_explained_variance) + y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon)) + y <- Bgy * g + Bxy * x + y.epsilon - w.model <- glm(x ~ k,df, family=binomial(link='logit')) + df <- data.table(x=x,y=y,g=g) - if( m < N){ + if(m < N){ df <- df[sample(nrow(df), m), x.obs := x] } else { df <- df[, x.obs := x] } - df[, x.obs := x.obs] + df <- df[,w_pred:=x] - w <- predict(w.model, df) + rnorm(N, 0, 1) - ## y = B0 + B1x + e + pg <- mean(g) + px <- mean(x) + accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2) - df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)] - return(df) -} + # this works because of conditional probability + accuracy_g0 <- prediction_accuracy / (pg*(accuracy_imbalance_ratio) + (1-pg)) + accuracy_g1 <- accuracy_imbalance_ratio * accuracy_g0 -schennach <- function(df){ + dfg0 <- df[g==0] + ng0 <- nrow(dfg0) + dfg1 <- df[g==1] + ng1 <- nrow(dfg1) - fwx <- glm(x.obs~w, df, family=binomial(link='logit')) - df[,xstar_pred := predict(fwx, df)] - gxt <- lm(y ~ xstar_pred+g, df) + dfg0 <- dfg0[sample(ng0, (1-accuracy_g0)*ng0), w_pred := (w_pred-1)**2] + dfg1 <- dfg1[sample(ng1, (1-accuracy_g1)*ng1), w_pred := (w_pred-1)**2] -} + df <- rbind(dfg0,dfg1) + w <- predict(glm(x ~ w_pred,data=df,family=binomial(link='logit')),type='response') + df <- df[,':='(w=w, w_pred = w_pred)] + return(df) +} parser <- arg_parser("Simulate data and fit corrected models") parser <- add_argument(parser, "--N", default=5000, help="number of observations of w") parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations") parser <- add_argument(parser, "--seed", default=432, help='seed for the rng') parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather') +parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.01) +parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73) +parser <- add_argument(parser, "--accuracy_imbalance_difference", help='how much more accurate is the predictive model for one class than the other?', default=0.3) + args <- parse_args(parser) B0 <- 0 Bxy <- 0.2 -Bgy <- 0 -Bkx <- 2 -Bgx <- 0 +Bgy <- -0.2 + +df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, args$seed, args$y_explained_variance, args$prediction_accuracy, args$accuracy_imbalance_difference) + +result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference) +outline <- run_simulation_depvar(df=df, result) -outline <- run_simulation(simulate_data(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed) - ,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed)) outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE) if(file.exists(args$outfile)){ diff --git a/simulations/03_depvar_differential.R b/simulations/03_depvar_differential.R new file mode 100644 index 0000000..d52afe7 --- /dev/null +++ b/simulations/03_depvar_differential.R @@ -0,0 +1,113 @@ +### EXAMPLE 1: demonstrates how measurement error can lead to a type sign error in a covariate +### What kind of data invalidates fong + tyler? +### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign. +### Even when you include the proxy variable in the regression. +### But with some ground truth and multiple imputation, you can fix it. + +library(argparser) +library(mecor) +library(ggplot2) +library(data.table) +library(filelock) +library(arrow) +library(Amelia) +library(Zelig) +library(predictionError) +options(amelia.parallel="no", + amelia.ncpus=1) +setDTthreads(40) + +source("simulation_base.R") + +## SETUP: +### we want to estimate x -> y; x is MAR +### we have x -> k; k -> w; x -> w is used to predict x via the model w. +### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments +### The labels x are binary, but the model provides a continuous predictor + +### simulation: +#### how much power do we get from the model in the first place? (sweeping N and m) +#### + +## one way to do it is by adding correlation to x.obs and y that isn't in w. +## in other words, the model is missing an important feature of x.obs that's related to y. +simulate_data <- function(N, m, B0, Bxy, Bgy, seed, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){ + set.seed(seed) + # make w and y dependent + g <- rbinom(N, 1, 0.5) + x <- rbinom(N, 1, 0.5) + + ystar <- Bgy * g + Bxy * x + y <- rbinom(N,1,logistic(ystar)) + + # glm(y ~ x + g, family="binomial") + + df <- data.table(x=x,y=y,ystar=ystar,g=g) + + if(m < N){ + df <- df[sample(nrow(df), m), y.obs := y] + } else { + df <- df[, y.obs := y] + } + + df <- df[,w_pred:=y] + + pg <- mean(g) + + accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2) + + # this works because of conditional probability + accuracy_g0 <- prediction_accuracy / (pg*(accuracy_imbalance_ratio) + (1-pg)) + accuracy_g1 <- accuracy_imbalance_ratio * accuracy_g0 + + dfg0 <- df[g==0] + ng0 <- nrow(dfg0) + dfg1 <- df[g==1] + ng1 <- nrow(dfg1) + + dfg0 <- dfg0[sample(ng0, (1-accuracy_g0)*ng0), w_pred := (w_pred-1)**2] + dfg1 <- dfg1[sample(ng1, (1-accuracy_g1)*ng1), w_pred := (w_pred-1)**2] + + df <- rbind(dfg0,dfg1) + + wmod <- glm(y.obs ~ w_pred,data=df[!is.null(y.obs)],family=binomial(link='logit')) + w <- predict(wmod,df,type='response') + + df <- df[,':='(w=w)] + + return(df) +} + +parser <- arg_parser("Simulate data and fit corrected models") +parser <- add_argument(parser, "--N", default=5000, help="number of observations of w") +parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations") +parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng') +parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather') +parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005) +parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73) +parser <- add_argument(parser, "--accuracy_imbalance_difference", help='how much more accurate is the predictive model for one class than the other?', default=0.3) + +args <- parse_args(parser) + +B0 <- 0 +Bxy <- 0.2 +Bgy <- -0.2 + +df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, args$seed, args$prediction_accuracy, args$accuracy_imbalance_difference) + +result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference) + +outline <- run_simulation_depvar(df=df, result) + + +outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE) +if(file.exists(args$outfile)){ + logdata <- read_feather(args$outfile) + logdata <- rbind(logdata,as.data.table(outline)) +} else { + logdata <- as.data.table(outline) +} + +print(outline) +write_feather(logdata, args$outfile) +unlock(outfile_lock) diff --git a/simulations/Makefile b/simulations/Makefile index 97b5894..01c34fc 100644 --- a/simulations/Makefile +++ b/simulations/Makefile @@ -17,12 +17,12 @@ example_1.feather: example_1_jobs sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_1_jobs example_2_jobs: example_2.R - grid_sweep.py --command "Rscript example_2.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"]}' --outfile example_2_jobs + grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"]}' --outfile example_2_jobs example_2.feather: example_2_jobs rm -f example_2.feather sbatch --wait --verbose --array=1-3000 run_simulation.sbatch 0 example_2_jobs -# sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_2_jobs + sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_2_jobs example_2_B_jobs: example_2_B.R grid_sweep.py --command "Rscript example_2_B.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2_B.feather"]}' --outfile example_2_B_jobs diff --git a/simulations/simulation_base.R b/simulations/simulation_base.R index 345d14e..a73ed79 100644 --- a/simulations/simulation_base.R +++ b/simulations/simulation_base.R @@ -4,9 +4,164 @@ options(amelia.parallel="no", amelia.ncpus=1) library(Amelia) library(Zelig) +library(stats4) + + +## This uses the pseudolikelihood approach from Carroll page 349. +## assumes MAR +## assumes differential error, but that only depends on Y +## inefficient, because pseudolikelihood +logistic.correction.pseudo <- function(df){ + p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T) + p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T) + + nll <- function(B0, Bxy, Bgy){ + probs <- (1 - p0.est) + (p1.est + p0.est - 1)*plogis(B0 + Bxy * df$x + Bgy * df$g) + + part1 = sum(log(probs[df$w_pred == 1])) + part2 = sum(log(1-probs[df$w_pred == 0])) + + return(-1*(part1 + part2)) + } + + mlefit <- stats4::mle(minuslogl = nll, start = list(B0=0, Bxy=0.0, Bgy=0.0)) + return(mlefit) + +} + +## This uses the likelihood approach from Carroll page 353. +## assumes that we have a good measurement error model +logistic.correction.liklihood <- function(df){ + + ## liklihood for observed responses + nll <- function(B0, Bxy, Bgy, gamma0, gamma_y, gamma_g){ + df.obs <- df[!is.na(y.obs)] + p.y.obs <- plogis(B0 + Bxy * df.obs$x + Bgy*df.obs$g) + p.y.obs[df.obs$y==0] <- 1-p.y.obs[df.obs$y==0] + p.s.obs <- plogis(gamma0 + gamma_y * df.obs$y + gamma_g*df.obs$g) + p.s.obs[df.obs$w_pred==0] <- 1 - p.s.obs[df.obs$w_pred==0] + + p.obs <- p.s.obs * p.y.obs + + df.unobs <- df[is.na(y.obs)] + + p.unobs.1 <- plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g)*plogis(gamma0 + gamma_y + gamma_g*df.unobs$g) + p.unobs.0 <- (1-plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g))*plogis(gamma0 + gamma_g*df.unobs$g) + p.unobs <- p.unobs.1 + p.unobs.0 + p.unobs[df.unobs$w_pred==0] <- 1 - p.unobs[df.unobs$w_pred==0] + + p <- c(p.obs, p.unobs) + + return(-1*(sum(log(p)))) + } + + mlefit <- stats4::mle(minuslogl = nll, start = list(B0=1, Bxy=0,Bgy=0, gamma0=5, gamma_y=0, gamma_g=0)) + + return(mlefit) +} + logistic <- function(x) {1/(1+exp(-1*x))} +run_simulation_depvar <- function(df, result){ + + accuracy <- df[,mean(w_pred==y)] + result <- append(result, list(accuracy=accuracy)) + + (model.true <- glm(y ~ x + g, data=df,family=binomial(link='logit'))) + true.ci.Bxy <- confint(model.true)['x',] + true.ci.Bgy <- confint(model.true)['g',] + + result <- append(result, list(Bxy.est.true=coef(model.true)['x'], + Bgy.est.true=coef(model.true)['g'], + Bxy.ci.upper.true = true.ci.Bxy[2], + Bxy.ci.lower.true = true.ci.Bxy[1], + Bgy.ci.upper.true = true.ci.Bgy[2], + Bgy.ci.lower.true = true.ci.Bgy[1])) + + (model.feasible <- glm(y.obs~x+g,data=df,family=binomial(link='logit'))) + + feasible.ci.Bxy <- confint(model.feasible)['x',] + result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'], + Bxy.ci.upper.feasible = feasible.ci.Bxy[2], + Bxy.ci.lower.feasible = feasible.ci.Bxy[1])) + + feasible.ci.Bgy <- confint(model.feasible)['g',] + result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'], + Bgy.ci.upper.feasible = feasible.ci.Bgy[2], + Bgy.ci.lower.feasible = feasible.ci.Bgy[1])) + + (model.naive <- glm(w_pred~x+g, data=df, family=binomial(link='logit'))) + + naive.ci.Bxy <- confint(model.naive)['x',] + naive.ci.Bgy <- confint(model.naive)['g',] + + result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'], + Bgy.est.naive=coef(model.naive)['g'], + Bxy.ci.upper.naive = naive.ci.Bxy[2], + Bxy.ci.lower.naive = naive.ci.Bxy[1], + Bgy.ci.upper.naive = naive.ci.Bgy[2], + Bgy.ci.lower.naive = naive.ci.Bgy[1])) + + + (model.naive.cont <- lm(w~x+g, data=df)) + naivecont.ci.Bxy <- confint(model.naive.cont)['x',] + naivecont.ci.Bgy <- confint(model.naive.cont)['g',] + + ## my implementatoin of liklihood based correction + mod.caroll.lik <- logistic.correction.liklihood(df) + coef <- coef(mod.caroll.lik) + ci <- confint(mod.caroll.lik) + + result <- append(result, + list(Bxy.est.mle = coef['Bxy'], + Bxy.ci.upper.mle = ci['Bxy','97.5 %'], + Bxy.ci.lower.mle = ci['Bxy','2.5 %'], + Bgy.est.mle = coef['Bgy'], + Bgy.ci.upper.mle = ci['Bgy','97.5 %'], + Bgy.ci.lower.mle = ci['Bgy','2.5 %'])) + + + ## my implementatoin of liklihood based correction + mod.caroll.pseudo <- logistic.correction.pseudo(df) + coef <- coef(mod.caroll.pseudo) + ci <- confint(mod.caroll.pseudo) + + result <- append(result, + list(Bxy.est.pseudo = coef['Bxy'], + Bxy.ci.upper.pseudo = ci['Bxy','97.5 %'], + Bxy.ci.lower.pseudo = ci['Bxy','2.5 %'], + Bgy.est.pseudo = coef['Bgy'], + Bgy.ci.upper.pseudo = ci['Bgy','97.5 %'], + Bgy.ci.lower.pseudo = ci['Bgy','2.5 %'])) + + + # amelia says use normal distribution for binary variables. + amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w_pred')) + mod.amelia.k <- zelig(y.obs~x+g, model='ls', data=amelia.out.k$imputations, cite=FALSE) + (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE)) + + est.x.mi <- coefse['x','Estimate'] + est.x.se <- coefse['x','Std.Error'] + result <- append(result, + list(Bxy.est.amelia.full = est.x.mi, + Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se, + Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se + )) + + est.g.mi <- coefse['g','Estimate'] + est.g.se <- coefse['g','Std.Error'] + + result <- append(result, + list(Bgy.est.amelia.full = est.g.mi, + Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se, + Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se + )) + + return(result) + +} + run_simulation <- function(df, result){ accuracy <- df[,mean(w_pred==x)] @@ -48,19 +203,7 @@ run_simulation <- function(df, result){ Bgy.ci.lower.naive = naive.ci.Bgy[1])) - ## multiple imputation when k is observed - ## amelia does great at this one. - noms <- c() - if(length(unique(df$x.obs)) <=2){ - noms <- c(noms, 'x.obs') - } - - if(length(unique(df$g)) <=2){ - noms <- c(noms, 'g') - } - - - amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=noms) + amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred')) mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE) (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))