114 lines
4.1 KiB
R
114 lines
4.1 KiB
R
### EXAMPLE 1: demonstrates how measurement error can lead to a type sign error in a covariate
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### What kind of data invalidates fong + tyler?
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### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
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### Even when you include the proxy variable in the regression.
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### But with some ground truth and multiple imputation, you can fix it.
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library(argparser)
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library(mecor)
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library(ggplot2)
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library(data.table)
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library(filelock)
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library(arrow)
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library(Amelia)
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library(Zelig)
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library(predictionError)
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options(amelia.parallel="no",
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amelia.ncpus=1)
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setDTthreads(40)
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source("simulation_base.R")
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## SETUP:
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### we want to estimate x -> y; x is MAR
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### we have x -> k; k -> w; x -> w is used to predict x via the model w.
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### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
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### The labels x are binary, but the model provides a continuous predictor
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### simulation:
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#### how much power do we get from the model in the first place? (sweeping N and m)
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####
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## one way to do it is by adding correlation to x.obs and y that isn't in w.
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## in other words, the model is missing an important feature of x.obs that's related to y.
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simulate_data <- function(N, m, B0, Bxy, Bgy, seed, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
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set.seed(seed)
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# make w and y dependent
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g <- rbinom(N, 1, 0.5)
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x <- rbinom(N, 1, 0.5)
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ystar <- Bgy * g + Bxy * x
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y <- rbinom(N,1,logistic(ystar))
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# glm(y ~ x + g, family="binomial")
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df <- data.table(x=x,y=y,ystar=ystar,g=g)
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if(m < N){
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df <- df[sample(nrow(df), m), y.obs := y]
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} else {
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df <- df[, y.obs := y]
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}
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df <- df[,w_pred:=y]
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pg <- mean(g)
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accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
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# this works because of conditional probability
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accuracy_g0 <- prediction_accuracy / (pg*(accuracy_imbalance_ratio) + (1-pg))
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accuracy_g1 <- accuracy_imbalance_ratio * accuracy_g0
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dfg0 <- df[g==0]
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ng0 <- nrow(dfg0)
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dfg1 <- df[g==1]
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ng1 <- nrow(dfg1)
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dfg0 <- dfg0[sample(ng0, (1-accuracy_g0)*ng0), w_pred := (w_pred-1)**2]
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dfg1 <- dfg1[sample(ng1, (1-accuracy_g1)*ng1), w_pred := (w_pred-1)**2]
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df <- rbind(dfg0,dfg1)
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wmod <- glm(y.obs ~ w_pred,data=df[!is.null(y.obs)],family=binomial(link='logit'))
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w <- predict(wmod,df,type='response')
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df <- df[,':='(w=w)]
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return(df)
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}
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parser <- arg_parser("Simulate data and fit corrected models")
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parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
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parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations")
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parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng')
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parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
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parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005)
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parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
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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)
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args <- parse_args(parser)
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B0 <- 0
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Bxy <- 0.2
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Bgy <- -0.2
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df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, args$seed, args$prediction_accuracy, args$accuracy_imbalance_difference)
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result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference)
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outline <- run_simulation_depvar(df=df, result)
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outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
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if(file.exists(args$outfile)){
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logdata <- read_feather(args$outfile)
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logdata <- rbind(logdata,as.data.table(outline))
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} else {
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logdata <- as.data.table(outline)
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}
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print(outline)
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write_feather(logdata, args$outfile)
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unlock(outfile_lock)
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