A Variational Maximization-Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects
A Variational Maximization-Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects
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DOI：
10.1007/s11336-017-9555-z
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发表时间：
2017-09-01
期刊：
影响因子：
3
通讯作者：
Rabe-Hesketh, Sophia
中科院分区：
文献类型：
--
作者：
Jeon, Minjeong;Rijmen, Frank;Rabe-Hesketh, Sophia
本文提出了一种变分极大化-极大化算法，用于具有交叉随机效应的广义线性混合模型的近似极大似然估计（例如，具有随机项目、随机评分者或随机特定于测验的效应的项目反应模型）。该方法是基于一个因子化的变分近似的潜变量分布给定的观测变量，它创建了一个下界的对数边际似然。关于因子化的分布以及模型参数，下限被最大化。该算法将高维复杂积分问题转化为二维积分问题。我们将自适应高斯-厄米求积法结合变分法，以提高计算效率。数值研究表明，在小样本条件下，所考虑的算法优于拉普拉斯近似。
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.