@@ -363,7 +363,7 @@ We sampled $N=50k$ samples of $X$, $Z$, and $W$ as independent standard Gaussia
% It can be / was modified by changing the outcome producing mechanism. For other experiments we changed the outcome generating mechanism so that the outcome was assigned value 1 if
The \emph{default} decision maker in the data fits a logistic regression model $Y \sim\invlogit(\beta_xx+\beta_zz)$ using the training set. The decisions were assigned by computing the quantile the subject belongs to. The quantile was obtained as the inverse cdf of ... .
$T=1$ to $R$ percent of subjects given by the leniency with highest probability of $Y=1$ in the test set.
$T=1$ to $R$ percent of subjects given by the leniency with highest probability of $Y=1$ in the test set. For all subjects for which $T=0$ we set $Y=1$.
We used a number of different decision mechanism. A \emph{limited} works as the default but uses regression model $Y \sim\invlogit(\beta_xx)$. Hence it is unable to observe $Z$.
