+### EXAMPLE 2: demonstrates how measurement error can lead to a type sign error in a covariate
+### 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)
+
+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)
+####
+logistic <- function(x) {1/(1+exp(-1*x))}
+
+simulate_latent_cocause <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
+ set.seed(seed)
+
+ ## the true value of x
+
+ g <- rbinom(N, 1, 0.5)
+ xprime <- Bgx * g + rnorm(N,0,1)
+
+ k <- Bkx*xprime + rnorm(N,0,3)
+
+ x <- as.integer(logistic(scale(xprime)) > 0.5)
+
+ y <- Bxy * x + Bgy * g + rnorm(N, 0, 2) + B0
+ df <- data.table(x=x,k=k,y=y,g=g)
+
+ if( m < N){
+ df <- df[sample(nrow(df), m), x.obs := x]
+ } else {
+ df <- df[, x.obs := x]
+ }
+
+ w.model <- glm(x ~ k,df, family=binomial(link='logit'))
+ w <- predict(w.model,data.frame(k=k)) + rnorm(N,0,1)
+ ## y = B0 + B1x + e
+
+ df[,':='(w=w, w_pred = as.integer(w>0.5))]
+ return(df)
+}
+
+
+parser <- arg_parser("Simulate data and fit corrected models")
+parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=100, 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_B.feather')
+args <- parse_args(parser)
+
+
+B0 <- 0
+Bxy <- 0.2
+Bgy <- 0
+Bkx <- 3.2
+Bgx <- 0
+
+df <- simulate_latent_cocause(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
+
+outline <- run_simulation(df
+ ,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=0, 'Bkx'=Bkx, 'Bgx'=0, 'seed'=args$seed))
+
+outfile_lock <- lock(paste0(args$outfile, '_lock'))
+if(file.exists(args$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)
+
+## for(N in Ns){
+## print(N)
+## for(m in ms){
+## if(N>m){
+## for(seed in seeds){
+## rows <- append(rows, list(run_simulation(N, m, B0, Bxy, Bkx, seed)))
+## }
+## }
+## }
+## }
+
+
+## run_simulation <- function(N, m, B0, Bxy, Bkx, seed){
+## result <- list()
+## df <- simulate_latent_cocause(N, m, B0, Bxy, Bkx, seed)
+
+## result <- append(result, list(N=N,
+## m=m,
+## B0=B0,
+## Bxy=Bxy,
+## Bkx=Bkx,
+## seed=seed))
+
+## (correlation <- cor(df$w,df$x,method='spearman'))
+## result <- append(result, list(correlation=correlation))
+
+## (accuracy <- mean(df$x == df$w_pred))
+
+## result <- append(result, list(accuracy=accuracy))
+
+## (model.true <- lm(y ~ x, data=df))
+
+## (cor(resid(model.true),df$w))
+
+## true.ci.Bxy <- confint(model.true)['x',]
+
+## result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
+## Bxy.ci.upper.true = true.ci.Bxy[2],
+## Bxy.ci.lower.true = true.ci.Bxy[1]))
+
+## (model.naive <- lm(y~w, data=df))
+
+## (model.feasible <- lm(y~x.obs,data=df))
+
+## feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
+## result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
+## Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
+## Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
+
+
+## naive.ci.Bxy <- confint(model.naive)['w',]
+
+## result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
+## Bxy.ci.upper.naive = naive.ci.Bxy[2],
+## Bxy.ci.lower.naive = naive.ci.Bxy[1]))
+
+
+## ## multiple imputation when k is observed
+
+## amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'), noms=c("x.obs"),lgstc=c('w'))
+## mod.amelia.k <- zelig(y~x.obs, model='ls', data=amelia.out.k$imputations, cite=FALSE)
+## (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
+
+## est.x.mi <- coefse['x.obs','Estimate']
+## est.x.se <- coefse['x.obs','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
+## ))
+
+
+## ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
+## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","k","w_pred"),noms=c("x.obs"),lgstc=c('w'))
+## mod.amelia.nok <- zelig(y~x.obs, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
+## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
+
+## est.x.mi <- coefse['x.obs','Estimate']
+## est.x.se <- coefse['x.obs','Std.Error']
+## result <- append(result,
+## list(Bxy.est.amelia.nok = est.x.mi,
+## Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
+## Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
+## ))
+
+## p <- v <- train <- rep(0,N)
+## M <- m
+## p[(M+1):(N)] <- 1
+## v[1:(M)] <- 1
+## df <- df[order(x.obs)]
+## y <- df[,y]
+## x <- df[,x.obs]
+## w <- df[,w]
+## (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=FALSE))
+
+## result <- append(result,
+## list(Bxy.est.gmm = gmm.res$beta[1,1],
+## Bxy.ci.upper.gmm = gmm.res$confint[1,2],
+## Bxy.ci.lower.gmm = gmm.res$confint[1,1]))
+
+## mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs), df, B=400, method='efficient')
+
+## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
+
+## result <- append(result, list(
+## Bxy.est.mecor = mecor.ci['Estimate'],
+## Bxy.upper.mecor = mecor.ci['UCI'],
+## Bxy.lower.mecor = mecor.ci['LCI'])
+## )
+
+
+## return(result)
+## }
+
projects / ml_measurement_error_public.git / blobdiff