Added, but didn't test the remaining robustness checks.

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

diff --git a/simulations/01_two_covariates.R b/simulations/01_two_covariates.R
index c52a3dc3c45e7d1769455adf17225d1b16a2aba3..cd688c7d4b34d2456302299bc284cfedceb2c3f3 100644 (file)
--- a/simulations/01_two_covariates.R
+++ b/simulations/01_two_covariates.R
@@ -1,8 +1,10 @@
-### 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.
+### 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)
@@ -12,9 +14,9 @@ library(filelock)
 library(arrow)
 library(Amelia)
 library(Zelig)
+
 library(predictionError)
-options(amelia.parallel="no",
-        amelia.ncpus=1)
+options(amelia.parallel="no", amelia.ncpus=1)
 
 source("simulation_base.R")
 
@@ -28,20 +30,18 @@ source("simulation_base.R")
 #### 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){
+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, Px=0.5, 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)
+    z <- rnorm(N,sd=0.5)
+                                        #    x.var.epsilon <- var(Bzx *z) * ((1-zx_explained_variance)/zx_explained_variance)
+    xprime <- Bzx * z + qlogis(Px)
+    x <- rbinom(N,1,plogis(xprime))
 
-    y.var.epsilon <- (var(Bgy * g) + var(Bxy *x) + 2*cov(Bxy*x,Bgy*g)) * ((1-y_explained_variance)/y_explained_variance)
+    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 <- Bgy * g + Bxy * x + y.epsilon
+    y <- Bzy * z + Bxy * x + y.epsilon
 
-    df <- data.table(x=x,xprime=xprime,y=y,g=g)
+    df <- data.table(x=x,y=y,z=z)
 
     if(m < N){
         df <- df[sample(nrow(df), m), x.obs := x]
@@ -49,33 +49,54 @@ simulate_data <- function(N, m, B0=0, Bxy=0.2, Bgy=-0.2, Bgx=0.2, y_explained_va
         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)]
+    ## 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=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)
+parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=200, 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, "--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, "--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 x on y', default=0.3)
+parser <- add_argument(parser, "--Px", help='Base rate of x', default=0.5)
 
+args <- parse_args(parser)
 B0 <- 0
-Bxy <- 0.2
-Bgy <- -0.2
-Bgx <- 0.5
+Px <- args$Px
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+Bzx <- args$Bzx
+
+df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, Bzx, Px, seed=args$seed + 500, y_explained_variance = args$y_explained_variance,  prediction_accuracy=args$prediction_accuracy)
 
-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)
+result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=Bzx, 'Bzy'=Bzy, 'Px'=Px, '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$outcome_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, 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))
+    logdata <- rbind(logdata,as.data.table(outline),fill=TRUE)
 } else {
     logdata <- as.data.table(outline)
 }
@@ -83,3 +104,4 @@ if(file.exists(args$outfile)){
 print(outline)
 write_feather(logdata, args$outfile)
 unlock(outfile_lock)
+