Flexible Modeling via a Hybrid Estimation Scheme in Generalized Mixed Models for Longitudinal Data

• Published in: Biometrics 2006-03, Vol.62 (1), p.159-167
• Main Authors: Leung Lai, Tze, Shih, Mei‐Chiung, Wong, Samuel Po‐Shing
• Format: Article
• Language: English
• Subjects: Animals; Approximation; Biometrics; biometry; Covariance matrices; Double exponential family; Drosophila; Estimating techniques; Estimation methods; fecundity; Fertility; fruit flies; Generalized mixed models; Hybrid method; Inference; Laplaces method; Likelihood Functions; Linear Models; Linear regression; Longitudinal data; Longitudinal Studies; Models, Statistical; Monte Carlo Method; Monte Carlo simulation; Parametric models; Regression analysis; Regression splines; Statistical analysis
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.1541-0420.2005.00391.x

To circumvent the computational complexity of likelihood inference in generalized mixed models that assume linear or more general additive regression models of covariate effects, Laplace's approximations to multiple integrals in the likelihood have been commonly used without addressing the issue of adequacy of the approximations for individuals with sparse observations. In this article, we propose a hybrid estimation scheme to address this issue. The likelihoods for subjects with sparse observations use Monte Carlo approximations involving importance sampling, while Laplace's approximation is used for the likelihoods of other subjects that satisfy a certain diagnostic check on the adequacy of Laplace's approximation. Because of its computational tractability, the proposed approach allows flexible modeling of covariate effects by using regression splines and model selection procedures for knot and variable selection. Its computational and statistical advantages are illustrated by simulation and by application to longitudinal data from a fecundity study of fruit flies, for which overdispersion is modeled via a double exponential family.