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Monte Carlo approximation through Gibbs output in generalized linear mixed models

Author

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  • Chan, Jennifer S.K.
  • Kuk, Anthony Y.C.
  • Yam, Carrie H.K.

Abstract

Geyer (J. Roy. Statist. Soc. 56 (1994) 291) proposed Monte Carlo method to approximate the whole likelihood function. His method is limited to choosing a proper reference point. We attempt to improve the method by assigning some prior information to the parameters and using the Gibbs output to evaluate the marginal likelihood and its derivatives through a Monte Carlo approximation. Vague priors are assigned to the parameters as well as the random effects within the Bayesian framework to represent a non-informative setting. Then the maximum likelihood estimates are obtained through the Newton Raphson method. Thus, out method serves as a bridge between Bayesian and classical approaches. The method is illustrated by analyzing the famous salamander mating data by generalized linear mixed models.

Suggested Citation

  • Chan, Jennifer S.K. & Kuk, Anthony Y.C. & Yam, Carrie H.K., 2005. "Monte Carlo approximation through Gibbs output in generalized linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 300-312, June.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:2:p:300-312
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    References listed on IDEAS

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    1. S. Choy & A. Smith, 1997. "Hierarchical models with scale mixtures of normal distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 205-221, June.
    2. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
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    Cited by:

    1. Chan, Jennifer S.K. & Leung, Doris Y.P. & Boris Choy, S.T. & Wan, Wai Y., 2009. "Nonignorable dropout models for longitudinal binary data with random effects: An application of Monte Carlo approximation through the Gibbs output," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4530-4545, October.
    2. Jennifer Chan & Wai Wan, 2011. "Bayesian approach to analysing longitudinal bivariate binary data with informative dropout," Computational Statistics, Springer, vol. 26(1), pages 121-144, March.

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