title: Logistic Regression with Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages.
abstract: Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss-Hermite. Many studies have investigated these methods' performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to anti-tobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages-SAS GLIMMIX Laplace and SuperMix Gaussian quadrature-perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes.
authors.affiliation: Institute for Health Research and Policy, University of Illinois at Chicago, 1747 W. Roosevelt Rd., Chicago, IL 60608.
authors.forename: Yoonsang
authors.initials: Y
authors.lastname: Kim
authors.forename: Young-Ku
authors.initials: YK
authors.lastname: Choi
authors.forename: Sherry
authors.initials: S
authors.lastname: Emery
keywords: Adaptive Gauss-Hermite integration; Antismoking advertising; Laplace approximation; Mixed-effects logistic regression; Penalized quasi-likelihood