A0290
Title: Misspecification matters: Prediction under misspecified random effects distributions in GLMMs
Authors: Quan Vu - Australian National University (Australia) [presenting]
Francis Hui - The Australian National University (Australia)
Samuel Muller - Macquarie University (Australia)
Alan Welsh - the Australian National University (Australia)
Abstract: The generalized linear mixed model (GLMM) is widely used in applied sciences because of its capability to model clustered data. One important aspect when dealing with GLMMs is the prediction of random effects and mean responses. There have been contradictory views in the literature on whether the normality assumption on the random effects significantly impacts the quality of the prediction with respect to mean squared prediction error (MSEP) when the underlying random effects are not normal. We investigate this problem by comparing the empirical best predictors of the random effects and the mean responses under a misspecified normal distribution against those under a correctly specified distribution, which is a mixture of normal distributions. Our findings indicate that the unconditional MSEPs for the random effects are higher under the incorrectly assumed normal distribution, when the true random effects distribution is very skewed or multimodal, especially when the cluster size is small. The conditional MSEPs for the random effects are also generally higher under the misspecified distribution, especially at the region closer to the mean of each component of the underlying mixture distribution (given this distribution is skewed or multimodal). These results demonstrate the importance of random effects specification to prediction in GLMMs.
