114 lines
5.3 KiB
R
114 lines
5.3 KiB
R
### EXAMPLE 2_b: demonstrates how measurement error can lead to a type
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### sign error in a covariate This is the same as example 2, only
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### instead of x->k we have k->x. Even when you have a good
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### predictor, if it's biased against a covariate you can get the
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### wrong sign. Even when you include the proxy variable in the
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### regression. But with some ground truth and multiple imputation,
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### 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", amelia.ncpus=1)
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source("irr_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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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){
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set.seed(seed)
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z <- rbinom(N, 1, 0.5)
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# x.var.epsilon <- var(Bzx *z) * ((1-zx_explained_variance)/zx_explained_variance)
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xprime <- Bzx * z #+ x.var.epsilon
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x <- rbinom(N,1,plogis(xprime))
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y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bxy*x,Bzy*z)) * ((1-y_explained_variance)/y_explained_variance)
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y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
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y <- Bzy * z + Bxy * x + y.epsilon
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df <- data.table(x=x,y=y,z=z)
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if(m < N){
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df <- df[sample(nrow(df), m), x.obs := x]
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} else {
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df <- df[, x.obs := x]
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}
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df[ (!is.na(x.obs)) ,x.obs.0 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
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df[ (!is.na(x.obs)) ,x.obs.1 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
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## how can you make a model with a specific accuracy?
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w0 =(1-x)**2 + (-1)**(1-x) * prediction_accuracy
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## how can you make a model with a specific accuracy, with a continuous latent variable.
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# now it makes the same amount of mistake to each point, probably
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# add mean0 noise to the odds.
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w.noisey.odds = rlogis(N,qlogis(w0))
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df[,w := plogis(w.noisey.odds)]
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df[,w_pred:=as.integer(w > 0.5)]
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(mean(df$x==df$w_pred))
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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=1000, help="number of observations of w")
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parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
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parser <- add_argument(parser, "--seed", default=57, help='seed for the rng')
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parser <- add_argument(parser, "--outfile", help='output file', default='example_1.feather')
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parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.05)
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# parser <- add_argument(parser, "--zx_explained_variance", help='what proportion of the variance of x can be explained by z?', default=0.3)
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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, "--coder_accuracy", help='how accurate is the predictive model?', default=0.8)
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parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
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parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~x")
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# parser <- add_argument(parser, "--rater_formula", help='formula for the true variable', default="x.obs~x")
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parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
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parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=-0.3)
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parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
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parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
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args <- parse_args(parser)
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B0 <- 0
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Bxy <- args$Bxy
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Bzy <- args$Bzy
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Bzx <- args$Bzx
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if (args$m < args$N){
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df <- simulate_data(args$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$coder_accuracy)
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result <- list('N'=args$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='')
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outline <- run_simulation(df, result, outcome_formula=as.formula(args$outcome_formula), proxy_formula=as.formula(args$proxy_formula), truth_formula=as.formula(args$truth_formula))
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outfile_lock <- lock(paste0(args$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),fill=TRUE)
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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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}
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