add mle methods from carroll
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@ -50,8 +50,8 @@ simulate_data <- function(N, m, B0=0, Bxy=0.2, Bgy=-0.2, Bgx=0.2, y_explained_va
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}
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df <- df[,w_pred:=x]
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df <- df[sample(1:N,(1-prediction_accuracy)*N),w_pred:=(w_pred-1)**2]
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w <- predict(glm(x ~ w_pred,data=df,family=binomial(link='logit')),type='response')
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df <- df[,':='(w=w, w_pred = w_pred)]
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return(df)
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}
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@ -61,15 +61,20 @@ parser <- add_argument(parser, "--N", default=500, help="number of observations
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parser <- add_argument(parser, "--m", default=100, 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_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=0.005)
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parser <- add_argument(parser, "--gx_explained_variance", help='what proportion of the variance of x can be explained by g?', default=0.15)
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parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
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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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Bgx <- 0.5
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Bgx <- 0.4
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df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, Bgx, seed=args$seed, y_explained_variance = 0.025, gx_explained_variance = 0.15)
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result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bgx'=Bgx, 'seed'=args$seed)
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df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, Bgx, seed=args$seed, y_explained_variance = args$y_explained_variance, gx_explained_variance = args$gx_explained_variance, prediction_accuracy=args$prediction_accuracy)
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result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bgx'=Bgx, 'seed'=args$seed, 'y_explained_variance' = args$y_explained_variance, 'gx_explained_variance' = args$gx_explained_variance, "prediction_accuracy"=args$prediction_accuracy)
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outline <- run_simulation(df, result)
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outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
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@ -31,68 +31,70 @@ source("simulation_base.R")
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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, Bkx, Bgx, seed, xy.explained.variance=0.01, u.explained.variance=0.1){
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simulate_data <- function(N, m, B0, Bxy, Bgy, seed, y_explained_variance=0.025, prediction_accuracy=0.73, accuracy_imbalance_difference=0.3){
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set.seed(seed)
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## the true value of x
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g <- rbinom(N, 1, 0.5)
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# make w and y dependent
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u <- rnorm(N,0,)
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g <- rbinom(N, 1, 0.5)
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x <- rbinom(N, 1, 0.5)
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xprime <- Bgx * g + rnorm(N,0,1)
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y.var.epsilon <- (var(Bgy * g) + var(Bxy *x) + 2*cov(Bgy*g,Bxy*x)) * ((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 <- Bgy * g + Bxy * x + y.epsilon
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k <- Bkx*xprime + rnorm(N,0,1.5) + 1.1*Bkx*u
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df <- data.table(x=x,y=y,g=g)
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x <- as.integer(logistic(scale(xprime)) > 0.5)
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y <- Bxy * x + Bgy * g + B0 + u + rnorm(N, 0, 1)
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df <- data.table(x=x,k=k,y=y,g=g)
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w.model <- glm(x ~ k,df, family=binomial(link='logit'))
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if( m < N){
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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[, x.obs := x.obs]
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df <- df[,w_pred:=x]
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w <- predict(w.model, df) + rnorm(N, 0, 1)
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## y = B0 + B1x + e
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pg <- mean(g)
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px <- mean(x)
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accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
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df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)]
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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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w <- predict(glm(x ~ w_pred,data=df,family=binomial(link='logit')),type='response')
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df <- df[,':='(w=w, w_pred = w_pred)]
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return(df)
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}
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schennach <- function(df){
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fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
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df[,xstar_pred := predict(fwx, df)]
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gxt <- lm(y ~ xstar_pred+g, 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=432, 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=0.01)
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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
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Bkx <- 2
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Bgx <- 0
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Bgy <- -0.2
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df <- simulate_data(args$N, args$m, B0, Bxy, Bgy, args$seed, args$y_explained_variance, args$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$accuracy_imbalance_difference)
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outline <- run_simulation_depvar(df=df, result)
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outline <- run_simulation(simulate_data(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
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,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))
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outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
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if(file.exists(args$outfile)){
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113
simulations/03_depvar_differential.R
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113
simulations/03_depvar_differential.R
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@ -0,0 +1,113 @@
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### 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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@ -17,12 +17,12 @@ example_1.feather: example_1_jobs
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sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_1_jobs
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example_2_jobs: example_2.R
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grid_sweep.py --command "Rscript example_2.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"]}' --outfile example_2_jobs
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grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"]}' --outfile example_2_jobs
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example_2.feather: example_2_jobs
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rm -f example_2.feather
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sbatch --wait --verbose --array=1-3000 run_simulation.sbatch 0 example_2_jobs
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# sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_2_jobs
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sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_2_jobs
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example_2_B_jobs: example_2_B.R
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grid_sweep.py --command "Rscript example_2_B.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2_B.feather"]}' --outfile example_2_B_jobs
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@ -4,9 +4,164 @@ options(amelia.parallel="no",
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amelia.ncpus=1)
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library(Amelia)
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library(Zelig)
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library(stats4)
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## This uses the pseudolikelihood approach from Carroll page 349.
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## assumes MAR
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## assumes differential error, but that only depends on Y
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## inefficient, because pseudolikelihood
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logistic.correction.pseudo <- function(df){
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p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
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p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
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nll <- function(B0, Bxy, Bgy){
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probs <- (1 - p0.est) + (p1.est + p0.est - 1)*plogis(B0 + Bxy * df$x + Bgy * df$g)
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part1 = sum(log(probs[df$w_pred == 1]))
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part2 = sum(log(1-probs[df$w_pred == 0]))
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return(-1*(part1 + part2))
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}
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mlefit <- stats4::mle(minuslogl = nll, start = list(B0=0, Bxy=0.0, Bgy=0.0))
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return(mlefit)
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}
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## This uses the likelihood approach from Carroll page 353.
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## assumes that we have a good measurement error model
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logistic.correction.liklihood <- function(df){
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## liklihood for observed responses
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nll <- function(B0, Bxy, Bgy, gamma0, gamma_y, gamma_g){
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df.obs <- df[!is.na(y.obs)]
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p.y.obs <- plogis(B0 + Bxy * df.obs$x + Bgy*df.obs$g)
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p.y.obs[df.obs$y==0] <- 1-p.y.obs[df.obs$y==0]
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p.s.obs <- plogis(gamma0 + gamma_y * df.obs$y + gamma_g*df.obs$g)
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p.s.obs[df.obs$w_pred==0] <- 1 - p.s.obs[df.obs$w_pred==0]
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p.obs <- p.s.obs * p.y.obs
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df.unobs <- df[is.na(y.obs)]
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p.unobs.1 <- plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g)*plogis(gamma0 + gamma_y + gamma_g*df.unobs$g)
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p.unobs.0 <- (1-plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g))*plogis(gamma0 + gamma_g*df.unobs$g)
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p.unobs <- p.unobs.1 + p.unobs.0
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p.unobs[df.unobs$w_pred==0] <- 1 - p.unobs[df.unobs$w_pred==0]
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p <- c(p.obs, p.unobs)
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return(-1*(sum(log(p))))
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}
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mlefit <- stats4::mle(minuslogl = nll, start = list(B0=1, Bxy=0,Bgy=0, gamma0=5, gamma_y=0, gamma_g=0))
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return(mlefit)
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}
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logistic <- function(x) {1/(1+exp(-1*x))}
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run_simulation_depvar <- function(df, result){
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accuracy <- df[,mean(w_pred==y)]
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result <- append(result, list(accuracy=accuracy))
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(model.true <- glm(y ~ x + g, data=df,family=binomial(link='logit')))
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true.ci.Bxy <- confint(model.true)['x',]
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true.ci.Bgy <- confint(model.true)['g',]
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result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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Bgy.est.true=coef(model.true)['g'],
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Bxy.ci.upper.true = true.ci.Bxy[2],
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Bxy.ci.lower.true = true.ci.Bxy[1],
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Bgy.ci.upper.true = true.ci.Bgy[2],
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Bgy.ci.lower.true = true.ci.Bgy[1]))
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(model.feasible <- glm(y.obs~x+g,data=df,family=binomial(link='logit')))
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feasible.ci.Bxy <- confint(model.feasible)['x',]
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result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
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Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
|
||||
Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
|
||||
|
||||
feasible.ci.Bgy <- confint(model.feasible)['g',]
|
||||
result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
|
||||
Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
|
||||
Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
|
||||
|
||||
(model.naive <- glm(w_pred~x+g, data=df, family=binomial(link='logit')))
|
||||
|
||||
naive.ci.Bxy <- confint(model.naive)['x',]
|
||||
naive.ci.Bgy <- confint(model.naive)['g',]
|
||||
|
||||
result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
|
||||
Bgy.est.naive=coef(model.naive)['g'],
|
||||
Bxy.ci.upper.naive = naive.ci.Bxy[2],
|
||||
Bxy.ci.lower.naive = naive.ci.Bxy[1],
|
||||
Bgy.ci.upper.naive = naive.ci.Bgy[2],
|
||||
Bgy.ci.lower.naive = naive.ci.Bgy[1]))
|
||||
|
||||
|
||||
(model.naive.cont <- lm(w~x+g, data=df))
|
||||
naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
|
||||
naivecont.ci.Bgy <- confint(model.naive.cont)['g',]
|
||||
|
||||
## my implementatoin of liklihood based correction
|
||||
mod.caroll.lik <- logistic.correction.liklihood(df)
|
||||
coef <- coef(mod.caroll.lik)
|
||||
ci <- confint(mod.caroll.lik)
|
||||
|
||||
result <- append(result,
|
||||
list(Bxy.est.mle = coef['Bxy'],
|
||||
Bxy.ci.upper.mle = ci['Bxy','97.5 %'],
|
||||
Bxy.ci.lower.mle = ci['Bxy','2.5 %'],
|
||||
Bgy.est.mle = coef['Bgy'],
|
||||
Bgy.ci.upper.mle = ci['Bgy','97.5 %'],
|
||||
Bgy.ci.lower.mle = ci['Bgy','2.5 %']))
|
||||
|
||||
|
||||
## my implementatoin of liklihood based correction
|
||||
mod.caroll.pseudo <- logistic.correction.pseudo(df)
|
||||
coef <- coef(mod.caroll.pseudo)
|
||||
ci <- confint(mod.caroll.pseudo)
|
||||
|
||||
result <- append(result,
|
||||
list(Bxy.est.pseudo = coef['Bxy'],
|
||||
Bxy.ci.upper.pseudo = ci['Bxy','97.5 %'],
|
||||
Bxy.ci.lower.pseudo = ci['Bxy','2.5 %'],
|
||||
Bgy.est.pseudo = coef['Bgy'],
|
||||
Bgy.ci.upper.pseudo = ci['Bgy','97.5 %'],
|
||||
Bgy.ci.lower.pseudo = ci['Bgy','2.5 %']))
|
||||
|
||||
|
||||
# amelia says use normal distribution for binary variables.
|
||||
amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w_pred'))
|
||||
mod.amelia.k <- zelig(y.obs~x+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
|
||||
(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
|
||||
|
||||
est.x.mi <- coefse['x','Estimate']
|
||||
est.x.se <- coefse['x','Std.Error']
|
||||
result <- append(result,
|
||||
list(Bxy.est.amelia.full = est.x.mi,
|
||||
Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
|
||||
Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
|
||||
))
|
||||
|
||||
est.g.mi <- coefse['g','Estimate']
|
||||
est.g.se <- coefse['g','Std.Error']
|
||||
|
||||
result <- append(result,
|
||||
list(Bgy.est.amelia.full = est.g.mi,
|
||||
Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
|
||||
Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
|
||||
))
|
||||
|
||||
return(result)
|
||||
|
||||
}
|
||||
|
||||
run_simulation <- function(df, result){
|
||||
|
||||
accuracy <- df[,mean(w_pred==x)]
|
||||
@ -48,19 +203,7 @@ run_simulation <- function(df, result){
|
||||
Bgy.ci.lower.naive = naive.ci.Bgy[1]))
|
||||
|
||||
|
||||
## multiple imputation when k is observed
|
||||
## amelia does great at this one.
|
||||
noms <- c()
|
||||
if(length(unique(df$x.obs)) <=2){
|
||||
noms <- c(noms, 'x.obs')
|
||||
}
|
||||
|
||||
if(length(unique(df$g)) <=2){
|
||||
noms <- c(noms, 'g')
|
||||
}
|
||||
|
||||
|
||||
amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=noms)
|
||||
amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
|
||||
mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
|
||||
(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user