86 lines
3.1 KiB
R
86 lines
3.1 KiB
R
### EXAMPLE 2_b: demonstrates how measurement error can lead to a type sign error in a covariate
|
|
### This is the same as example 2, only instead of x->k we have k->x.
|
|
### 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)
|
|
|
|
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)
|
|
####
|
|
|
|
simulate_data <- function(N, m, B0=0, Bxy=0.2, Bgy=-0.2, Bgx=0.2, y_explained_variance=0.025, gx_explained_variance=0.15, prediction_accuracy=0.73, seed=1){
|
|
set.seed(seed)
|
|
g <- rbinom(N, 1, 0.5)
|
|
|
|
x.var.epsilon <- var(Bgx *g) * ((1-gx_explained_variance)/gx_explained_variance)
|
|
x.epsilon <- rnorm(N,sd=sqrt(x.var.epsilon))
|
|
xprime <- Bgx * g + x.epsilon
|
|
x <- as.integer(logistic(scale(xprime)) > 0.5)
|
|
|
|
y.var.epsilon <- (var(Bgy * g) + var(Bxy *x) + 2*cov(Bxy*x,Bgy*g)) * ((1-y_explained_variance)/y_explained_variance)
|
|
y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
|
|
y <- Bgy * g + Bxy * x + y.epsilon
|
|
|
|
df <- data.table(x=x,xprime=xprime,y=y,g=g)
|
|
|
|
if(m < N){
|
|
df <- df[sample(nrow(df), m), x.obs := x]
|
|
} else {
|
|
df <- df[, x.obs := x]
|
|
}
|
|
|
|
df <- df[,w_pred:=x]
|
|
|
|
df <- df[sample(1:N,(1-prediction_accuracy)*N),w_pred:=(w_pred-1)**2]
|
|
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=500, 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=4321, 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 <- -0.2
|
|
Bgx <- 0.5
|
|
|
|
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)
|
|
outline <- run_simulation(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)
|