The effects of mixture distribution misspecification when fitting mixed-effects logistic models

Mixed-effects logistic models are often used to analyze binary response data which have been gathered in clusters, or groups. Responses are assumed to follow a logistic model with in clusters, with an intercept which varies across clusters according to a specified probability distribution G. In this paper we examine the performance of mixed-effects logistic regression analysis when a main component of the model, the mixture distribution, is misspecified. We show that, when the mixture distribution is misspecified, estimates of model parameters, including the effects of covariates, typically are asymptotically biased, i.e. inconsistent. However, we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small. These findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified.