title: Testing for misspecification in generalized linear mixed models.
abstract: Generalized linear mixed models have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research shows that the results obtained from these models are not always robust against departures from the assumptions on which they are based. Therefore, diagnostic tools for the detection of model misspecifications are of the utmost importance. In this paper, we propose 2 diagnostic tests that are based on 2 equivalent representations of the model information matrix. We evaluate the power of both tests using theoretical considerations as well as via simulation. In the simulations, the performance of the new tools is evaluated in many settings of practical relevance, focusing on misspecification of the random-effects structure. In all the scenarios, the results were encouraging, however, the tests also exhibited inflated Type I error rates when the sample size was small or moderate. Importantly, a parametric bootstrap version of the tests seems to overcome this problem, although more research in this direction may be needed. Finally, both tests were also applied to analyze a real case study in psychiatry.
authors.affiliation: Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Agoralaan 1, B3590 Diepenbeek, Belgium,. ariel.alonso@uhasselt.be
authors.forename: Ariel Alonso
authors.initials: AA
authors.lastname: Abad
authors.forename: Saskia
authors.initials: S
authors.lastname: Litière
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
mesh_terms: D000465:Algorithms; D014150:Antipsychotic Agents / Q000627:therapeutic use; D015982:Bias; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008137:Longitudinal Studies / Q000379:methods*; D016032:Randomized Controlled Trials as Topic; D018967:Risperidone / Q000627:therapeutic use; D012559:Schizophrenia / Q000188:drug therapy; D012984:Software; D016896:Treatment Outcome
chemical_list: D014150:Antipsychotic Agents; D018967:Risperidone