make first simulation with precise accuracies and explained variances

[ml_measurement_error_public.git] / simulations / 01_two_covariates.R

diff --git a/simulations/01_two_covariates.R b/simulations/01_two_covariates.R
new file mode 100644 (file)
index 0000000..c52a3dc
--- /dev/null
+++ b/simulations/01_two_covariates.R
@@ -0,0 +1,85 @@
+### 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)