An Approximate Restricted Likelihood Ratio Test for Variance Components in Generalized Linear Mixed Models

2019/06/07 by Stephanie T. Chen, Luo Xiao, Chen, Stephanie T. +3
Agricultural and Biological Sciences · Decision Sciences · Mathematics · #FOS: Computer and information sciences #Genetics and Plant Breeding #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1906.03320

openalex publication_date 2019/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalized linear mixed models (GLMMs) are used to model responses from exponential families with a combination of fixed and random effects. For variance components in GLMMs, we propose an approximate restricted likelihood ratio test that conducts testing on the working responses used in penalized quasi-likelihood estimation. This presents the hypothesis test in terms of normalized responses, allowing for application of existing testing methods for linear mixed models. Our test is flexible, computationally efficient, and outperforms several competitors. We illustrate the utility of the proposed method with an extensive simulation study and two data applications. An R package is provided.

Citations

• Maximum Likelihood for Generalized Linear Models with Nested Random Effects via High-Order, Multivariate Laplace Approximation
• Generalized linear mixed models: a practical guide for ecology and evolution

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