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Nested generalized linear mixed models: an orthodox best linear unbiased predictor approach
Author(s) -
Ma Renjun,
Jørgensen Bent
Publication year - 2007
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00603.x
Subject(s) - mathematics , estimator , best linear unbiased prediction , generalized linear mixed model , generalized linear model , range (aeronautics) , inference , exponential function , linear regression , parametric statistics , linear model , exponential family , statistics , computer science , artificial intelligence , mathematical analysis , selection (genetic algorithm) , materials science , composite material
Summary. We introduce a new class of generalized linear mixed models based on the Tweedie exponential dispersion model distributions, accommodating a wide range of discrete, continuous and mixed data. Using the best linear unbiased predictor of random effects, we obtain an optimal estimating function for the regression parameters in the sense of Godambe, allowing an efficient common fitting algorithm for the whole class. Although allowing full parametric inference, our main results depend only on the first‐ and second‐moment assumptions of unobserved random effects. In addition, we obtain consistent estimators for both regression and dispersion parameters. We illustrate the method by analysing the epilepsy data and cake baking data. Along with simulations and asymptotic justifications, this shows the usefulness of the method for analysis of clustered non‐normal data.