Logistic Regression With Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages
- 1 August 2013
- journal article
- research article
- Published by Informa UK Limited in The American Statistician
- Vol. 67 (3), 171-182
- https://doi.org/10.1080/00031305.2013.817357
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.Keywords
This publication has 21 references indexed in Scilit:
- The Effects of Smoking-Related Television Advertising on Smoking and Intentions to Quit Among Adults in the United States: 1999–2007American Journal of Public Health, 2012
- Accuracy of Laplace approximation for discrete response mixed modelsComputational Statistics & Data Analysis, 2008
- The Rise and Fall of Tobacco Control Media Campaigns, 1967–2006American Journal of Public Health, 2007
- A simulation study of sample size for multilevel logistic regression modelsBMC Medical Research Methodology, 2007
- Comparison of PQL and Laplace 6 estimates of hierarchical linear models when comparing groups of small incident rates in cluster randomised trialsComputational Statistics & Data Analysis, 2007
- Numerical integration in logistic-normal modelsComputational Statistics & Data Analysis, 2006
- The design of simulation studies in medical statisticsStatistics in Medicine, 2006
- Logistic regression with random coefficientsComputational Statistics & Data Analysis, 1994
- Laplace's approximation for nonlinear mixed modelsBiometrika, 1993
- Binomial random variate generationCommunications of the ACM, 1988