I know that both Pearson and Deviance residuals tend to be approximately normal for Poisson and Binomial model with large counts when standardized, so we can exploit that to perform the residual analysis. But I was told that we cannot expect the residuals to be normal when our model is Bernoulli or binomial model with small counts, i.e with counts <5. Is there any other conventional method to analyze the residual in such cases?
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You can use simulation see https://stats.stackexchange.com/questions/70558/diagnostic-plots-for-count-regression/248035#248035 – kjetil b halvorsen Mar 05 '19 at 15:22