Bayesian analysis is given of a random effects binary probit model that allows for heteroscedasticity. Real and simulated examples illustrate the approach and show that ignoring heteroscedasticity when it exists may lead to biased estimates and poor prediction. The computation is carried out by an efficient Markov chain Monte Carlo sampling scheme that generates the parameters in blocks. We use the Bayes factor, cross-validation of the predictive density, the deviance information criterion and Receiver Operating Characteristic (ROC) curves for model comparison.
Gu, Y., Fiebig, D., Cripps, E., & Kohn, R. (2009). Bayesian estimation of a random effects heteroscedastic probit model. Econometrics Journal, 12(2), 324-339. https://doi.org/10.1111/j.1368-423X.2009.00283.x