Exploring residuals for classification models

• Due their range ($[-1,1]$) limitations, the residuals $r_i$ are not very useful to explore the probability of observing $y_i$.

• If all explanatory variables are categorical with a limited number of categories the standard-normal approximation is likely if follow the following steps:

  • Divide the observed values in $K$ groups sharing the same predicted value $f_k$.
  • Average the residuals $r_i$ per group and standardizing them with $\sqrt{f_k(1-f_k)/n_k}$