Title: Missing covariate data in generalized linear mixed models with distribution-free random effects
Authors: Li Liu - Wuhan University (China)
Liming Xiang - Nanyang Technological University (Singapore) [presenting]
Abstract: Generalized linear mixed models are considered in which the random effects are free of parametric distributions and missing at random data are present in some covariates. To overcome the problem of missing data, we propose two novel methods: a penalized conditional likelihood method relying on the auxiliary variable that is independent of random effects, and a two-step procedure consisting of a pairwise likelihood for estimating fixed effects in the first step and a penalized conditional likelihood for estimating random effects in the second step, relying on the auxiliary variable that is associated with random effects. Our methods require no distribution assumption for random effects and allow a nonparametric error structure, thus providing great flexibility in capturing a board range of behaviours of both the error term and random effects. We show that the proposed estimators enjoy desirable properties such as consistency and asymptotically normality, and assess their finite sample performance through extensive simulation studies. The proposed methods are further illustrated using a longitudinal data set on forest health monitoring.