Model diagnostics is an integral part of model determination and an important part of the model diagnostics is residual analysis. We adapt and implement residuals considered in the literature for the probit, logistic and skew-probit links under binary regression. New latent residuals for the skew-probit link are proposed here. We have detected the presence of outliers using the residuals proposed here for different models in a simulated dataset and a real medical dataset.
"Latent residual analysis in binary regression with skewed link." Braz. J. Probab. Stat. 26 (4) 344 - 357, November 2012. https://doi.org/10.1214/11-BJPS143