+### 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, x_bias=-0.75){
+ 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 + B0
+ 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]
+ }
+
+ odds.y1 <- qlogis(prediction_accuracy) + x_bias*df[y==1]$x
+ odds.y0 <- qlogis(prediction_accuracy,lower.tail=F) + x_bias*df[y==0]$x
+
+ df[y==0,w:=plogis(rlogis(.N,odds.y0))]
+ df[y==1,w:=plogis(rlogis(.N,odds.y1))]
+
+ df[,w_pred := as.integer(w > 0.5)]
+
+ print(mean(df[x==0]$y == df[x==0]$w_pred))
+ print(mean(df[x==1]$y == df[x==1]$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=0.8)
+## parser <- add_argument(parser, "--x_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
+## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
+parser <- add_argument(parser, "--x_bias", help='how is the classifier biased?', default=0.75)
+parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.3)
+parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.3)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y+x")
+
+args <- parse_args(parser)
+
+B0 <- 0
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+
+
+if(args$m < args$N){
+ df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$x_bias)
+
+# result <- list('N'=args$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, 'x_bias_y0'=args$x_bias_y0,'x_bias_y1'=args$x_bias_y1,'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
+ 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$prediction_accuracy, 'x_bias'=args$x_bias,'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
+
+ outline <- run_simulation_depvar(df, result, outcome_formula = as.formula(args$outcome_formula), proxy_formula = as.formula(args$proxy_formula))
+
+ 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)
+}
projects / ml_measurement_error_public.git / commitdiff