title: Diagnosing misspecification of the random-effects distribution in mixed models.
abstract: It is traditionally assumed that the random effects in mixed models follow a multivariate normal distribution, making likelihood-based inferences more feasible theoretically and computationally. However, this assumption does not necessarily hold in practice which may lead to biased and unreliable results. We introduce a novel diagnostic test based on the so-called gradient function proposed by Verbeke and Molenberghs (2013) to assess the random-effects distribution. We establish asymptotic properties of our test and show that, under a correctly specified model, the proposed test statistic converges to a weighted sum of independent chi-squared random variables each with one degree of freedom. The weights, which are eigenvalues of a square matrix, can be easily calculated. We also develop a parametric bootstrap algorithm for small samples. Our strategy can be used to check the adequacy of any distribution for random effects in a wide class of mixed models, including linear mixed models, generalized linear mixed models, and non-linear mixed models, with univariate as well as multivariate random effects. Both asymptotic and bootstrap proposals are evaluated via simulations and a real data analysis of a randomized multicenter study on toenail dermatophyte onychomycosis.
authors.affiliation: I-BioStat, KU Leuven, Leuven, Belgium.|Department of Mathematics, Imperial College London, London, UK.
authors.forename: Reza
authors.initials: R
authors.lastname: Drikvandi
authors.affiliation: I-BioStat, KU Leuven, Leuven, Belgium.|I-BioStat, Universiteit Hasselt, Hasselt, Belgium.
authors.forename: Geert
authors.initials: G
authors.lastname: Verbeke
authors.affiliation: I-BioStat, KU Leuven, Leuven, Belgium.|I-BioStat, Universiteit Hasselt, Hasselt, Belgium.
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
mesh_terms: D000465:Algorithms; D003883:Arthrodermataceae; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005533:Foot Dermatoses; D006801:Humans; D016014:Linear Models; D015999:Multivariate Analysis; D009262:Nails / Q000382:microbiology; D014009:Onychomycosis / Q000382:microbiology; D016032:Randomized Controlled Trials as Topic
keywords: Asymptotic distribution; Eigenvalues; Gradient function; Longitudinal data; Parametric bootstrap; Random effects