+### 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("irr_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, Bzy=-0.2, Bzx=0.2, y_explained_variance=0.025, prediction_accuracy=0.73, coder_accuracy=0.9, seed=1){
+ set.seed(seed)
+ z <- rbinom(N, 1, 0.5)
+ # x.var.epsilon <- var(Bzx *z) * ((1-zx_explained_variance)/zx_explained_variance)
+ xprime <- Bzx * z #+ x.var.epsilon
+ x <- rbinom(N,1,plogis(xprime))
+
+ y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bxy*x,Bzy*z)) * ((1-y_explained_variance)/y_explained_variance)
+ y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
+ y <- Bzy * z + Bxy * x + y.epsilon
+
+ df <- data.table(x=x,y=y,z=z)
+
+ if(m < N){
+ df <- df[sample(nrow(df), m), x.obs := x]
+ } else {
+ df <- df[, x.obs := x]
+ }
+
+ df[ (!is.na(x.obs)) ,x.obs.0 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
+ df[ (!is.na(x.obs)) ,x.obs.1 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
+
+
+ ## how can you make a model with a specific accuracy?
+ w0 =(1-x)**2 + (-1)**(1-x) * prediction_accuracy
+
+ ## how can you make a model with a specific accuracy, with a continuous latent variable.
+ # now it makes the same amount of mistake to each point, probably
+ # add mean0 noise to the odds.
+
+ w.noisey.odds = rlogis(N,qlogis(w0))
+ df[,w := plogis(w.noisey.odds)]
+ df[,w_pred:=as.integer(w > 0.5)]
+ (mean(df$x==df$w_pred))
+ 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=57, help='seed for the rng')
+parser <- add_argument(parser, "--outfile", help='output file', default='example_1.feather')
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.05)
+# parser <- add_argument(parser, "--zx_explained_variance", help='what proportion of the variance of x can be explained by z?', default=0.3)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
+parser <- add_argument(parser, "--coder_accuracy", help='how accurate is the predictive model?', default=0.8)
+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~x")
+
+# parser <- add_argument(parser, "--rater_formula", help='formula for the true variable', default="x.obs~x")
+parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
+parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=-0.3)
+parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
+parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
+
+args <- parse_args(parser)
+B0 <- 0
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+Bzx <- args$Bzx
+
+if (args$m < args$N){
+
+ df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, Bzx, seed=args$seed + 500, y_explained_variance = args$y_explained_variance, prediction_accuracy=args$prediction_accuracy, coder_accuracy=args$coder_accuracy)
+
+ result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=Bzx, 'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, 'outcome_formula'=args$outcome_formula, 'truth_formula'=args$truth_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, 'coder_accuracy'=args$coder_accuracy, error='')
+
+ outline <- run_simulation(df, result, outcome_formula=as.formula(args$outcome_formula), proxy_formula=as.formula(args$proxy_formula), truth_formula=as.formula(args$truth_formula))
+
+ outfile_lock <- lock(paste0(args$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 / blobdiff