145 lines
4.0 KiB
R
145 lines
4.0 KiB
R
### EXAMPLE 2_b: demonstrates how measurement error can lead to a type sign error in a covariate
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### What kind of data invalidates fong + tyler?
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### This is the same as example 2, only instead of x->k we have k->x.
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### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
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### Even when you include the proxy variable in the regression.
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### But with some ground truth and multiple imputation, you can fix it.
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library(argparser)
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library(mecor)
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library(ggplot2)
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library(data.table)
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library(filelock)
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library(arrow)
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library(Amelia)
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library(Zelig)
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library(predictionError)
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options(amelia.parallel="no",
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amelia.ncpus=1)
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setDTthreads(40)
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source("simulation_base.R")
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## SETUP:
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### we want to estimate x -> y; x is MAR
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### we have x -> k; k -> w; x -> w is used to predict x via the model w.
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### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
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### The labels x are binary, but the model provides a continuous predictor
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### simulation:
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#### how much power do we get from the model in the first place? (sweeping N and m)
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####
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## one way to do it is by adding correlation to x.obs and y that isn't in w.
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## in other words, the model is missing an important feature of x.obs that's related to y.
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simulate_latent_cocause <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
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set.seed(seed)
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## the true value of x
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g <- rbinom(N, 1, 0.5)
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# make w and y dependent
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u <- rnorm(N,0,Bxy)
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xprime <- Bgx * g + rnorm(N,0,1)
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k <- Bkx*xprime + rnorm(N,0,1.5) + 1.1*Bkx*u
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x <- as.integer(logistic(scale(xprime)) > 0.5)
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y <- Bxy * x + Bgy * g + rnorm(N, 0, 1) + B0 + u
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df <- data.table(x=x,k=k,y=y,g=g)
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w.model <- glm(x ~ k,df, family=binomial(link='logit'))
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if( m < N){
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df <- df[sample(nrow(df), m), x.obs := x]
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} else {
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df <- df[, x.obs := x]
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}
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df[, x.obs := x.obs]
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w <- predict(w.model, df) + rnorm(N, 0, 1)
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## y = B0 + B1x + e
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df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)]
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return(df)
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}
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## simulate_latent_cocause_2 <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
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## set.seed(seed)
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## ## the true value of x
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## g <- rbinom(N, 1, 0.5)
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## # make w and y dependent
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## u <- rnorm(N,0,5)
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## xprime <- Bgx * g + rnorm(N,0,1)
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## k <- Bkx*xprime + rnorm(N,0,3)
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## x <- as.integer(logistic(scale(xprime+0.3)) > 0.5)
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## y <- Bxy * x + Bgy * g + rnorm(N, 0, 1) + B0 + u
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## df <- data.table(x=x,k=k,y=y,g=g)
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## w.model <- glm(x ~ k, df, family=binomial(link='logit'))
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## if( m < N){
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## df <- df[sample(nrow(df), m), x.obs := x]
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## } else {
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## df <- df[, x.obs := x]
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## }
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## w <- predict(w.model,data.frame(k=k)) + u
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## ## y = B0 + B1x + e
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## df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)]
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## return(df)
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## }
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schennach <- function(df){
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fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
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df[,xstar_pred := predict(fwx, df)]
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gxt <- lm(y ~ xstar_pred+g, df)
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}
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parser <- arg_parser("Simulate data and fit corrected models")
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parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
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parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations")
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parser <- add_argument(parser, "--seed", default=432, help='seed for the rng')
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parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
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args <- parse_args(parser)
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B0 <- 0
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Bxy <- 0.2
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Bgy <- 0
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Bkx <- 2
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Bgx <- 0
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outline <- run_simulation(simulate_latent_cocause(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
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,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))
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outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
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if(file.exists(args$outfile)){
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logdata <- read_feather(args$outfile)
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logdata <- rbind(logdata,as.data.table(outline))
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} else {
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logdata <- as.data.table(outline)
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}
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print(outline)
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write_feather(logdata, args$outfile)
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unlock(outfile_lock)
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