## print(mean(df[z==1]$x == df[z==1]$w_pred))
## print(mean(df$w_pred == df$x))
+
resids <- resid(lm(y~x + z))
- odds.x1 <- qlogis(prediction_accuracy) + y_bias*qlogis(pnorm(resids[x==1])) + z_bias * qlogis(pnorm(z,sd(z)))
- odds.x0 <- qlogis(prediction_accuracy,lower.tail=F) + y_bias*qlogis(pnorm(resids[x==0])) + z_bias * qlogis(pnorm(z,sd(z)))
+ odds.x1 <- qlogis(prediction_accuracy) + y_bias*qlogis(pnorm(resids[x==1])) + z_bias * qlogis(pnorm(z[x==1],sd(z)))
+ odds.x0 <- qlogis(prediction_accuracy,lower.tail=F) + y_bias*qlogis(pnorm(resids[x==0])) + z_bias * qlogis(pnorm(z[x==0],sd(z)))
## acc.x0 <- p.correct[df[,x==0]]
## acc.x1 <- p.correct[df[,x==1]]