X-Git-Url: https://code.communitydata.science/ml_measurement_error_public.git/blobdiff_plain/6057688060b5bf2a94f2b96b65b275a91991c0f3..e41d11afb9a80180feff844666e3ee463d20a7cd:/simulations/example_2_binary.R diff --git a/simulations/example_2_binary.R b/simulations/example_2_binary.R new file mode 100644 index 0000000..0e0d65c --- /dev/null +++ b/simulations/example_2_binary.R @@ -0,0 +1,169 @@ +### 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) + +options(amelia.parallel="multicore", + amelia.ncpus=40) + +## SETUP: +### we want to estimate g -> y and x -> y; g is observed, x is MAR +### we have k -> x; g -> x; g->k; k is used to predict x via the model w. +### we have k -> w; x -> w; w is observed. +### for illustration, g is binary (e.g., gender==male). +### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments +### Whether a comment is "racial harassment" depends on context, like the kind of person (i.e.,) the race of the person making the comment +### e.g., a Black person saying "n-word" is less likely to be racial harassement than if a white person does it. +### Say we have a language model that predicts "racial harassment," but it doesn't know the race of the writer. +### Our content analyzers can see signals of the writer's race (e.g., a profile or avatar). So our "ground truth" takes this into accont. +### Our goal is to predict an outcome (say that someone gets banned from the platform) as a function of whether they made a racial harassing comment and of their race. + +### 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) + k <- rnorm(N, 0, 1) + xprime <- Bkx*k + Bgx * g + x <- rbinom(N, 1, logistic(xprime - mean(xprime))) + w.model <- glm(x ~ k,family='binomial') + w <- as.integer(predict(w.model,data.frame(k=k),type='response') > 0.5) + ## y = B0 + B1x + e + y <- Bxy * x + Bgy * g + rnorm(N, 0, 1) + B0 + df <- data.table(x=x,k=k,y=y,w=w,g=g) + if( m < N){ + df <- df[sample(nrow(df), m), x.obs := x] + } else { + df <- df[, x.obs := x] + } + + return(df) +} + + +run_simulation <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){ + result <- list() + df <- simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed) + + result <- append(result, list(N=N, + m=m, + B0=B0, + Bxy=Bxy, + Bgy=Bgy, + Bkx=Bkx, + seed=seed)) + + accuracy <- df[,.(mean(w==x))]$V1 + result <- append(result, list(accuracy=accuracy)) + + model.true <- lm(y ~ x + g, data=df) + true.ci.Bxy <- confint(model.true)['x',] + true.ci.Bgy <- confint(model.true)['g',] + + result <- append(result, list(Bxy.est.true=coef(model.true)['x'], + Bgy.est.true=coef(model.true)['g'], + Bxy.ci.upper.true = true.ci.Bxy[2], + Bxy.ci.lower.true = true.ci.Bxy[1], + Bgy.ci.upper.true = true.ci.Bgy[2], + Bgy.ci.lower.true = true.ci.Bgy[1])) + + + model.naive <- lm(y~w+g, data=df) + + naive.ci.Bxy <- confint(model.naive)['w',] + naive.ci.Bgy <- confint(model.naive)['g',] + + result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'], + Bgy.est.naive=coef(model.naive)['g'], + Bxy.ci.upper.naive = naive.ci.Bxy[2], + Bxy.ci.lower.naive = naive.ci.Bxy[1], + Bgy.ci.upper.naive = naive.ci.Bgy[2], + Bgy.ci.lower.naive = naive.ci.Bgy[1])) + + + ## multiple imputation when k is observed + amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x'),noms=c("x.obs","w","g")) + mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE) + coefse <- combine_coef_se(mod.amelia.k, messages=FALSE) + + 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 + )) + + 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 + )) + + ## 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"), noms=c("x.obs","w",'g')) + mod.amelia.nok <- zelig(y~x.obs+g, 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 + )) + + est.g.mi <- coefse['g','Estimate'] + est.g.se <- coefse['g','Std.Error'] + + result <- append(result, + list(Bgy.est.amelia.nok = est.g.mi, + Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se, + Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se + )) + + return(result) +} + +Ns <- c(100, 200, 300, 400, 500, 1000, 2500, 5000, 7500) +ms <- c(30, 50, 100, 200, 300, 500) +B0 <- 0 +Bxy <- 1 +Bgy <- 0.3 +Bkx <- 3 +Bgx <- -4 +seeds <- 1:100 + +rows <- list() + +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, Bgy, Bkx, Bgx, seed))) + } + } + } +} + +result <- rbindlist(rows) +write_feather(result, "example_2_simulation.feather")