Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics
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Publication:6407497
DOI10.1016/J.SPL.2022.109691zbMATH Open1524.62347arXiv2208.05301MaRDI QIDQ6407497
Aishwarya Bhaskaran, Matt P. Wand
Publication date: 10 August 2022
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.
Characterization and structure theory for multivariate probability distributions; copulas (62H05) Generalized linear models (logistic models) (62J12) Characterization and structure theory of statistical distributions (62E10)
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