166 lines
6.6 KiB
R
166 lines
6.6 KiB
R
### EXAMPLE 1: 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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### 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_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
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set.seed(seed)
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# make w and y dependent
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z <- rbinom(N, 1, 0.5)
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x <- rbinom(N, 1, Bzx * z + 0.5)
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y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bzy*z,Bxy*x)) * ((1-y_explained_variance)/y_explained_variance)
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y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
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y <- Bzy * z + Bxy * x + y.epsilon
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df <- data.table(x=x,y=y,z=z)
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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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## px <- mean(x)
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## accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
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## # this works because of conditional probability
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## accuracy_x0 <- prediction_accuracy / (px*(accuracy_imbalance_ratio) + (1-px))
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## accuracy_x1 <- accuracy_imbalance_ratio * accuracy_x0
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## x0 <- df[x==0]$x
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## x1 <- df[x==1]$x
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## nx1 <- nrow(df[x==1])
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## nx0 <- nrow(df[x==0])
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## yx0 <- df[x==0]$y
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## yx1 <- df[x==1]$y
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# tranform yz0.1 into a logistic distribution with mean accuracy_z0
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## acc.x0 <- plogis(0.5*scale(yx0) + qlogis(accuracy_x0))
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## acc.x1 <- plogis(1.5*scale(yx1) + qlogis(accuracy_x1))
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## w0x0 <- (1-x0)**2 + (-1)**(1-x0) * acc.x0
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## w0x1 <- (1-x1)**2 + (-1)**(1-x1) * acc.x1
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pz <- mean(z)
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accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
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# this works because of conditional probability
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accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
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accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
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z0x0 <- df[(z==0) & (x==0)]$x
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z0x1 <- df[(z==0) & (x==1)]$x
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z1x0 <- df[(z==1) & (x==0)]$x
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z1x1 <- df[(z==1) & (x==1)]$x
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yz0x0 <- df[(z==0) & (x==0)]$y
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yz0x1 <- df[(z==0) & (x==1)]$y
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yz1x0 <- df[(z==1) & (x==0)]$y
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yz1x1 <- df[(z==1) & (x==1)]$y
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nz0x0 <- nrow(df[(z==0) & (x==0)])
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nz0x1 <- nrow(df[(z==0) & (x==1)])
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nz1x0 <- nrow(df[(z==1) & (x==0)])
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nz1x1 <- nrow(df[(z==1) & (x==1)])
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yz1 <- df[z==1]$y
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yz1 <- df[z==1]$y
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# tranform yz0.1 into a logistic distribution with mean accuracy_z0
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acc.z0x0 <- plogis(0.5*scale(yz0x0) + qlogis(accuracy_z0))
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acc.z0x1 <- plogis(0.5*scale(yz0x1) + qlogis(accuracy_z0))
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acc.z1x0 <- plogis(1.5*scale(yz1x0) + qlogis(accuracy_z1))
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acc.z1x1 <- plogis(1.5*scale(yz1x1) + qlogis(accuracy_z1))
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w0z0x0 <- (1-z0x0)**2 + (-1)**(1-z0x0) * acc.z0x0
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w0z0x1 <- (1-z0x1)**2 + (-1)**(1-z0x1) * acc.z0x1
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w0z1x0 <- (1-z1x0)**2 + (-1)**(1-z1x0) * acc.z1x0
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w0z1x1 <- (1-z1x1)**2 + (-1)**(1-z1x1) * acc.z1x1
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##perrorz0 <- w0z0*(pyz0)
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##perrorz1 <- w0z1*(pyz1)
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w0z0x0.noisy.odds <- rlogis(nz0x0,qlogis(w0z0x0))
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w0z0x1.noisy.odds <- rlogis(nz0x1,qlogis(w0z0x1))
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w0z1x0.noisy.odds <- rlogis(nz1x0,qlogis(w0z1x0))
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w0z1x1.noisy.odds <- rlogis(nz1x1,qlogis(w0z1x1))
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df[(z==0)&(x==0),w:=plogis(w0z0x0.noisy.odds)]
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df[(z==0)&(x==1),w:=plogis(w0z0x1.noisy.odds)]
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df[(z==1)&(x==0),w:=plogis(w0z1x0.noisy.odds)]
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df[(z==1)&(x==1),w:=plogis(w0z1x1.noisy.odds)]
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df[,w_pred:=as.integer(w > 0.5)]
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print(mean(df[z==0]$x == df[z==0]$w_pred))
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print(mean(df[z==1]$x == df[z==1]$w_pred))
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print(mean(df$w_pred == df$x))
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return(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=1400, help="number of observations of w")
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parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
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parser <- add_argument(parser, "--seed", default=50, 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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parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.01)
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parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
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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)
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parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=0.3)
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parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
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args <- parse_args(parser)
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B0 <- 0
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Bxy <- 0.3
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Bzy <- args$Bzy
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if(args$m < args$N){
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df <- simulate_data(args$N, args$m, B0, Bxy, args$Bzx, Bzy, args$seed, args$y_explained_variance, args$prediction_accuracy, args$accuracy_imbalance_difference)
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result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=args$Bzx, 'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, error='')
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outline <- run_simulation(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~x+z+y+x:y, truth_formula=x~z)
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outfile_lock <- lock(paste0(args$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), fill=TRUE)
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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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}
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