+ ## probablity of an error is correlated with 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
+
+ ## z0x0 <- df[(z==0) & (x==0)]$x
+ ## z0x1 <- df[(z==0) & (x==1)]$x
+ ## z1x0 <- df[(z==1) & (x==0)]$x
+ ## z1x1 <- df[(z==1) & (x==1)]$x
+
+ ## yz0x0 <- df[(z==0) & (x==0)]$y
+ ## yz0x1 <- df[(z==0) & (x==1)]$y
+ ## yz1x0 <- df[(z==1) & (x==0)]$y
+ ## yz1x1 <- df[(z==1) & (x==1)]$y
+
+ ## nz0x0 <- nrow(df[(z==0) & (x==0)])
+ ## nz0x1 <- nrow(df[(z==0) & (x==1)])
+ ## nz1x0 <- nrow(df[(z==1) & (x==0)])
+ ## nz1x1 <- nrow(df[(z==1) & (x==1)])
+
+ ## yz1 <- df[z==1]$y
+ ## yz1 <- df[z==1]$y
+
+ ## # tranform yz0.1 into a logistic distribution with mean accuracy_z0
+ ## acc.z0x0 <- plogis(0.5*scale(yz0x0) + qlogis(accuracy_z0))
+ ## acc.z0x1 <- plogis(0.5*scale(yz0x1) + qlogis(accuracy_z0))
+ ## acc.z1x0 <- plogis(1.5*scale(yz1x0) + qlogis(accuracy_z1))
+ ## acc.z1x1 <- plogis(1.5*scale(yz1x1) + qlogis(accuracy_z1))
+
+ ## w0z0x0 <- (1-z0x0)**2 + (-1)**(1-z0x0) * acc.z0x0
+ ## w0z0x1 <- (1-z0x1)**2 + (-1)**(1-z0x1) * acc.z0x1
+ ## w0z1x0 <- (1-z1x0)**2 + (-1)**(1-z1x0) * acc.z1x0
+ ## w0z1x1 <- (1-z1x1)**2 + (-1)**(1-z1x1) * acc.z1x1