Flexible Modelling of Small Area Counts Using Log-Gamma Random Effects
James Brown (University of Technology Sydney)
Jarod Lee and James Brown (UTS)
Nikos Tzavidis (University of Southampton)
Generalised Linear Mixed Models (GLMMs) are widely used in model-based small area estimation, where domain specific sample is not large enough to support direct estimates of adequate precision. By including random effects, GLMMs are able to produce reliable estimates by borrowing strength across areas, increasing the effective sample size. In typical applications, random effects are assumed to be Gaussian distributed, although the assumption is not necessary. There has been a lot of interest in flexible modelling of random effects, including using M-quantile, t-distribution, mixture distribution, semi-nonparametric distribution and h-likelihood, among others. In this talk, we propose using log-Gamma random effects which are negatively skewed but Gaussian in the limit. We call our approach the “conjugate GLMMs” as it induces closed-form likelihood, rendering estimation and prediction straightforward using the EM algorithm and best prediction respectively. We discuss a pseudolikelihood approach for accommodating weights when data come from complex surveys. The performance of conjugate GLMMs and GLMMs are also compared under a wide variety of true random effect distributions in a simulation study, with small area counts as the target of inference.