On the use of a penalized quasilikelihood information criterion for generalized linear mixed models

Information criteria are commonly used for joint fixed and random effects selection in mixed models. While information criteria are straightforward to implement, a major difficulty in applying them is that they are typically based on maximum likelihood estimates, but calculating such estimates for one candidate mixed model, let alone multiple models, presents a major computational challenge. To overcome this hurdle, we study penalized quasilikelihood estimation and use it as the basis for performing fast joint selection. Under a general framework, we show that penalized quasilikelihood estimation produces consistent estimates of the true parameters. We then propose a new penalized quasilikelihood information criterion whose distinguishing feature is the way it accounts for model complexity in the random effects, since penalized quasilikelihood estimation effectively treats the random effects as fixed. We demonstrate that the criterion asymptotically identifies the true set of important fixed and random effects. Simulations show that the quasilikelihood information criterion performs competitively with and sometimes better than common maximum likelihood information criteria for joint selection, while offering substantial reductions in computation time.