## 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, x_bias=-0.75){
+simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, z_bias=-0.75){
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,1,0.5)
ystar <- Bzy * z + Bxy * x + B0
y <- rbinom(N,1,plogis(ystar))
df <- df[, y.obs := y]
}
- odds.y1 <- qlogis(prediction_accuracy) + x_bias*df[y==1]$x
- odds.y0 <- qlogis(prediction_accuracy,lower.tail=F) + x_bias*df[y==0]$x
+ odds.y1 <- qlogis(prediction_accuracy) + z_bias*df[y==1]$z
+ odds.y0 <- qlogis(prediction_accuracy,lower.tail=F) + z_bias*df[y==0]$z
df[y==0,w:=plogis(rlogis(.N,odds.y0))]
df[y==1,w:=plogis(rlogis(.N,odds.y1))]
parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
parser <- add_argument(parser, "--seed", default=17, help='seed for the rng')
-parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
-parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005)
-parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.8)
-## parser <- add_argument(parser, "--x_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
-## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
-parser <- add_argument(parser, "--x_bias", help='how is the classifier biased?', default=0.75)
-parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.3)
-parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.3)
+parser <- add_argument(parser, "--outfile", help='output file', default='example_4.feather')
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.79)
+## parser <- add_argument(parser, "--z_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
+## parser <- add_argument(parser, "--z_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
+parser <- add_argument(parser, "--z_bias", help='how is the classifier biased?', default=1.5)
+parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.1)
+parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.1)
+parser <- add_argument(parser, "--B0", help='coeffficient of z on y', default=-0.1)
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+x")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y+z")
args <- parse_args(parser)
-B0 <- 0
+B0 <- args$B0
Bxy <- args$Bxy
Bzy <- args$Bzy
if(args$m < args$N){
- df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$x_bias)
+ df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$z_bias)
-# result <- list('N'=args$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$prediction_accuracy, 'x_bias'=args$x_bias,'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$prediction_accuracy, 'z_bias_y0'=args$z_bias_y0,'z_bias_y1'=args$z_bias_y1,'outcome_formula' = args$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, 'z_bias'=args$z_bias,'outcome_formula' = args$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))