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Maximum Likelihood Estimation Using Laplace Approximation in Poisson GLMMs
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 Title & Authors
Maximum Likelihood Estimation Using Laplace Approximation in Poisson GLMMs
Ha, Il-Do;
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 Abstract
Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.
 Keywords
H-likelihood;laplace approximation;marginal likelihood;generalized linear mixed models;random effects;
 Language
English
 Cited by
 References
1.
Barndorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic techniques for use in Statistics, Chapman and Hall, New York

2.
Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems (with discussion). Statistical Science, 10, 3–66

3.
Booth, J. G. and Hobert, J. P. (1999). Maximum generalized linear mixed model likelihood with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society B, 61, 265–285 crossref(new window)

4.
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9–25

5.
Efron, B. (1996). Empirical Bayes methods for combining likelihoods (with discussion). Journal of the American Statistical Association, 91, 538–565

6.
Gaver, D. P. and O'Muircheartaigh, I. G. (1987). Robust empirical Bayes analysis of event rates, Technometrics, 29, 1–15

7.
Gueorguieva, R. (2001). A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family, Statistical Modelling, 1, 177–193

8.
Ha, I. D., Lee, Y. and Song, J.-K. (2001). Hierarchical likelihood approach for frailty models, Biometrika, 88, 233–243

9.
Ha, I. D., Lee, Y. and MacKenzie, G. (2007). Model selection for multi-component frailty models, Statistics in Medicine, 26, 4790–4807 crossref(new window)

10.
Huber, P., Ronchetti, E. and Victoria-Feser, M.-P. (2004). Estimation of generalized linear latent variable models, Journal of the Royal Statistical Society B, 66, 893–908 crossref(new window)

11.
Jiang, J. (2007). Linear and generalized linear mixed models and their applications, Springer, New York

12.
Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society B, 58, 619–678

13.
Lee, Y. and Nelder, J. A. (2001). Hierarchical generalized linear models: a synthesis of generalized linear models, random-effect models and structured dispersions, Biometrika, 88, 987–1006 crossref(new window)

14.
Lee, Y., Nelder, J. A. and Pawitan (2006). Generalized linear models with random effects, Chapman and Hall, New York

15.
Nelder, J. A. and Wedderburn (1972). Generalized linear models (with discussion), Journal of the Royal Statistical Society A, 135, 370–384

16.
Shun, Z. (1997). Another look at the salamander mating data: a modified Laplace approximation approach, Journal of the American Statistical Association, 92, 341–349

17.
Thall, P. F. and Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion, Biometrics, 46, 657–671