Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics

2022/08/10 by Aishwarya Bhaskaran, M. P. Wand, Bhaskaran, Aishwarya +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2208.05301

openalex publication_date 2022/08/10 · openalex created_date 2022/08/12 · openalex updated_date 2026/07/28

Abstract

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically normal distributions with asymptotic mutual independence between fixed effects, random effects covariance and dispersion parameters. The dispersion parameter maximum likelihood estimator has a particularly simple asymptotic distribution which enables straightforward valid likelihood-based inference.

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