124 lines
4.5 KiB
R
124 lines
4.5 KiB
R
### EXAMPLE 1: demonstrates how measurement error can lead to a type sign error in a covariate
|
|
### What kind of data invalidates fong + tyler?
|
|
### 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)
|
|
setDTthreads(40)
|
|
|
|
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)
|
|
####
|
|
|
|
## one way to do it is by adding correlation to x.obs and y that isn't in w.
|
|
## in other words, the model is missing an important feature of x.obs that's related to y.
|
|
simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
|
|
set.seed(seed)
|
|
# make w and y dependent
|
|
z <- rbinom(N, 1, 0.5)
|
|
x <- rbinom(N, 1, 0.5)
|
|
|
|
ystar <- Bzy * z + Bxy * x
|
|
y <- rbinom(N,1,plogis(ystar))
|
|
|
|
# glm(y ~ x + z, family="binomial")
|
|
|
|
df <- data.table(x=x,y=y,ystar=ystar,z=z)
|
|
|
|
if(m < N){
|
|
df <- df[sample(nrow(df), m), y.obs := y]
|
|
} else {
|
|
df <- df[, y.obs := y]
|
|
}
|
|
|
|
df <- df[,w_pred:=y]
|
|
|
|
pz <- mean(z)
|
|
|
|
accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
|
|
|
|
# this works because of conditional probability
|
|
accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
|
|
accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
|
|
|
|
|
|
yz0 <- df[z==0]$y
|
|
yz1 <- df[z==1]$y
|
|
nz1 <- nrow(df[z==1])
|
|
nz0 <- nrow(df[z==0])
|
|
|
|
acc_z0 <- plogis(0.7*scale(yz0) + qlogis(accuracy_z0))
|
|
acc_z1 <- plogis(1.3*scale(yz1) + qlogis(accuracy_z1))
|
|
|
|
w0z0 <- (1-yz0)**2 + (-1)**(1-yz0) * acc_z0
|
|
w0z1 <- (1-yz1)**2 + (-1)**(1-yz1) * acc_z1
|
|
|
|
w0z0.noisy.odds <- rlogis(nz0,qlogis(w0z0))
|
|
w0z1.noisy.odds <- rlogis(nz1,qlogis(w0z1))
|
|
df[z==0,w:=plogis(w0z0.noisy.odds)]
|
|
df[z==1,w:=plogis(w0z1.noisy.odds)]
|
|
|
|
df[,w_pred:=as.integer(w > 0.5)]
|
|
|
|
print(mean(df[y==0]$y == df[y==0]$w_pred))
|
|
print(mean(df[y==1]$y == df[y==1]$w_pred))
|
|
print(mean(df$w_pred == df$y))
|
|
|
|
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=500, help="m the number of ground truth observations")
|
|
parser <- add_argument(parser, "--seed", default=17, help='seed for the rng')
|
|
parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
|
|
parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005)
|
|
parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
|
|
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)
|
|
|
|
args <- parse_args(parser)
|
|
|
|
B0 <- 0
|
|
Bxy <- 0.7
|
|
Bzy <- -0.7
|
|
|
|
if(args$m < args$N){
|
|
df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$accuracy_imbalance_difference)
|
|
|
|
result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference)
|
|
|
|
outline <- run_simulation_depvar(df, result, outcome_formula = y ~ x + z, proxy_formula = w_pred ~ y*x + y*z + z*x)
|
|
|
|
outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
|
|
|
|
if(file.exists(args$outfile)){
|
|
logdata <- read_feather(args$outfile)
|
|
logdata <- rbind(logdata,as.data.table(outline),fill=TRUE)
|
|
} else {
|
|
logdata <- as.data.table(outline)
|
|
}
|
|
|
|
print(outline)
|
|
write_feather(logdata, args$outfile)
|
|
unlock(outfile_lock)
|
|
}
|