Add exploratory data analysis to come up with a real-data example.

[ml_measurement_error_public.git] / simulations / 03_depvar_differential.R

diff --git a/simulations/03_depvar_differential.R b/simulations/03_depvar_differential.R
index 872931f4c426a4680bb1aad03699668c90264c39..7b920ba6af6c7b6bfe7ed1cf962910767ab8e384 100644 (file)
--- a/simulations/03_depvar_differential.R
+++ b/simulations/03_depvar_differential.R
@@ -31,13 +31,14 @@ source("simulation_base.R")
 
 ## 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.
 
 ## 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, accuracy_imbalance_difference=0.3){
+simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, x_bias=-0.75){

     set.seed(seed)
     set.seed(seed)

+

     # make w and y dependent
     z <- rbinom(N, 1, 0.5)
     x <- rbinom(N, 1, 0.5)
 
     # make w and y dependent
     z <- rbinom(N, 1, 0.5)
     x <- rbinom(N, 1, 0.5)
 

-    ystar <- Bzy * z + Bxy * x
+    ystar <- Bzy * z + Bxy * x + B0

     y <- rbinom(N,1,plogis(ystar))
 
     # glm(y ~ x + z, family="binomial")
     y <- rbinom(N,1,plogis(ystar))
 
     # glm(y ~ x + z, family="binomial")


@@ -49,40 +50,18 @@ simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, ac
     } else {
         df <- df[, y.obs := y]
     }
     } else {
         df <- df[, y.obs := y]
     }

-
-    df <- df[,w_pred:=y]
-
-    pz <- mean(z)
-
-    accuracy_imbalance_ratio <- (prediction_accuracy + accuracy_imbalance_difference/2) / (prediction_accuracy - accuracy_imbalance_difference/2)
-
-    # this works because of conditional probability
-    accuracy_z0 <- prediction_accuracy / (pz*(accuracy_imbalance_ratio) + (1-pz))
-    accuracy_z1 <- accuracy_imbalance_ratio * accuracy_z0
-
-
-    yz0 <- df[z==0]$y
-    yz1 <- df[z==1]$y
-    nz1 <- nrow(df[z==1])
-    nz0 <- nrow(df[z==0])
-
-    acc_z0 <- plogis(0.7*scale(yz0) + qlogis(accuracy_z0))
-    acc_z1 <- plogis(1.3*scale(yz1) + qlogis(accuracy_z1))
-    
-    w0z0 <- (1-yz0)**2 + (-1)**(1-yz0) * acc_z0
-    w0z1 <- (1-yz1)**2 + (-1)**(1-yz1) * acc_z1

     
     

-    w0z0.noisy.odds <- rlogis(nz0,qlogis(w0z0))
-    w0z1.noisy.odds <- rlogis(nz1,qlogis(w0z1))
-    df[z==0,w:=plogis(w0z0.noisy.odds)]
-    df[z==1,w:=plogis(w0z1.noisy.odds)]
+    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

 
 

-    df[,w_pred:=as.integer(w > 0.5)]
+    df[y==0,w:=plogis(rlogis(.N,odds.y0))]
+    df[y==1,w:=plogis(rlogis(.N,odds.y1))]

 
 

-    print(mean(df[y==0]$y == df[y==0]$w_pred))
-    print(mean(df[y==1]$y == df[y==1]$w_pred))
-    print(mean(df$w_pred == df$y))
+    df[,w_pred := as.integer(w > 0.5)]

 
 

+    print(mean(df[x==0]$y == df[x==0]$w_pred))
+    print(mean(df[x==1]$y == df[x==1]$w_pred))
+    print(mean(df$w_pred == df$y))

     return(df)
 }
 
     return(df)
 }
 


@@ -92,21 +71,29 @@ parser <- add_argument(parser, "--m", default=500, help="m the number of ground
 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, "--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=0.73)
-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)
+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, "--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")

 
 args <- parse_args(parser)
 
 B0 <- 0
 
 args <- parse_args(parser)
 
 B0 <- 0

-Bxy <- 0.7
-Bzy <- -0.7
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+

 
 if(args$m < args$N){
 
 if(args$m < args$N){

-    df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$accuracy_imbalance_difference)
+    df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$x_bias_y0, args$x_bias_y1)

 
 

-    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$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference)
+#    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$x_bias,'x_bias'=args$x_bias,'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)

 
 

-    outline <- run_simulation_depvar(df, result, outcome_formula = y ~ x + z, proxy_formula = w_pred ~ y*x + y*z + z*x)
+    outline <- run_simulation_depvar(df, result, outcome_formula = as.formula(args$outcome_formula), proxy_formula = as.formula(args$proxy_formula))

 
     outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
 
 
     outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)