Abstract
Generalized linear mixed models are now popular in the animal breeding and biostatistics literature as these models allow inference on fixed and random effects for the exponential family of data distributions. In animal breeding, particular attention is directed towards variances of the random effects. We investigate three methods for marginal inference on variance components in binary data, including (1) the conventional expectation-maximization (EM) type algorithm, (2) Laplace's method, and (3) "exact" Gibbs sampling methods. A simulation study involving probit animal models was used to compare the modal estimates computed under the three methods. It was found that EM estimates were badly biased downwards in comparison to Laplacian estimates. An application of all methods within a repeated measures probit analysis of mastitis incidence in dairy cows suggests that Laplacian and Gibbs sampling posterior marginal modes are somewhat congruent in moderately sized data sets, although the tail of the posterior density was lighter for the Laplacian approximation.
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Recommended Citation
Tempelman, Robert J.
(1995).
"BAYESIAN INFERENCE ON VARIANCE COMPONENTS IN GENERALIZED LINEAR MIXED MODELS: AN EVALUATION OF DIFFERENT METHODS,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1334
BAYESIAN INFERENCE ON VARIANCE COMPONENTS IN GENERALIZED LINEAR MIXED MODELS: AN EVALUATION OF DIFFERENT METHODS
Generalized linear mixed models are now popular in the animal breeding and biostatistics literature as these models allow inference on fixed and random effects for the exponential family of data distributions. In animal breeding, particular attention is directed towards variances of the random effects. We investigate three methods for marginal inference on variance components in binary data, including (1) the conventional expectation-maximization (EM) type algorithm, (2) Laplace's method, and (3) "exact" Gibbs sampling methods. A simulation study involving probit animal models was used to compare the modal estimates computed under the three methods. It was found that EM estimates were badly biased downwards in comparison to Laplacian estimates. An application of all methods within a repeated measures probit analysis of mastitis incidence in dairy cows suggests that Laplacian and Gibbs sampling posterior marginal modes are somewhat congruent in moderately sized data sets, although the tail of the posterior density was lighter for the Laplacian approximation.
