A Variational Maximization-Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects

作     者：Jeon, Minjeong Rijmen, Frank Rabe-Hesketh, Sophia 

作者机构：Univ Calif Los Angeles Los Angeles CA USA Amer Inst Res Washington DC USA Univ Calif Berkeley Berkeley CA 94720 USA 

出 版 物：《PSYCHOMETRIKA》 (心理测量学)

年 卷 期：2017年第82卷第3期

页      面：693-716页

核心收录：

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 04[教育学] 0701[理学-数学] 

主　　题：variational approximation lower bound Kullback-Leibler divergence EM algorithm VMM algorithm adaptive quadrature GLMM crossed random effects 

摘      要：We present a variational maximization-maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss-Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation.