## one way to do it is by adding correlation to x.obs and y that isn't in w.
## in other words, the model is missing an important feature of x.obs that's related to y.
-simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, log.likelihood.gain = 0.1){
+simulate_data <- function(N, m, B0, Bxy, Bzy, Bzx, seed, prediction_accuracy=0.73, log.likelihood.gain = 0.1){
set.seed(seed)
set.seed(seed)
# make w and y dependent
- z <- rbinom(N, 1, 0.5)
- x <- rbinom(N, 1, 0.5)
+ z <- rnorm(N, sd=0.5)
+ x <- rbinom(N, 1, plogis(Bzx*z))
ystar <- Bzy * z + Bxy * x + B0
y <- rbinom(N,1,plogis(ystar))
## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.01)
parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.01)
+parser <- add_argument(parser, "--Bzx", help='coeffficient of z on x', default=-0.5)
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~y")
B0 <- 0
Bxy <- args$Bxy
Bzy <- args$Bzy
-
+Bzx <- args$Bzx
if(args$m < args$N){
- df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy)
+ df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, Bzx, args$seed, args$prediction_accuracy)
# result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'x_bias_y0'=args$x_bias_y0,'x_bias_y1'=args$x_bias_y1,'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
- result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
+ result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'Bzx'=Bzx,'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
outline <- run_simulation_depvar(df, result, outcome_formula = as.formula(args$outcome_formula), proxy_formula = as.formula(args$proxy_formula))