Assessing the performance of variational methods for mixed logistic regression models

Abstract

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived that results in a considerable simplification of the maximization problem in that it does not require the numerical evaluation of integrals over the random effects. We assess the performance of the variational method for the mixed logistic regression model in a simulation study and an empirical data example, and compare it to Laplace's method. The results indicate that the variational method is a viable choice for estimating the fixed effects of the mixed logistic regression model under the condition that the number of outcomes within each cluster is sufficiently high.

Keywords:

• Mixed models
• Logistic regression
• Variational methods
• Lower bound approximation

MSC :

• 62J12
• 62P15
• 62E17

Acknowledgements

Frank Rijmen was partly supported by the Fund for Scientific Research Flanders and Jiří Vomlel by the Ministry of Education of the Czech Republic under the projects nr. 1M0572 and nr. 2C06019.