[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2009.16.6.971

Maximum Likelihood Estimation Using Laplace Approximation in Poisson GLMMs

Ha, Il-Do (Department of Asset Management, Daegu Haany University)

Publication Information

Communications for Statistical Applications and Methods / v.16, no.6, 2009 , pp. 971-978 More about this Journal

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;

Citations & Related Records

Reference

1	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 DOI ScienceOn
2	Lee, Y., Nelder, J. A. and Pawitan (2006). Generalized linear models with random effects, Chapman and Hall, New York
3	Nelder, J. A. and Wedderburn (1972). Generalized linear models (with discussion), Journal of the Royal Statistical Society A, 135, 370–384
4	Shun, Z. (1997). Another look at the salamander mating data: a modified Laplace approximation approach, Journal of the American Statistical Association, 92, 341–349
5	Thall, P. F. and Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion, Biometrics, 46, 657–671
6	Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems (with discussion). Statistical Science, 10, 3–66
7	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 DOI ScienceOn
8	Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9–25
9	Efron, B. (1996). Empirical Bayes methods for combining likelihoods (with discussion). Journal of the American Statistical Association, 91, 538–565
10	Gaver, D. P. and O'Muircheartaigh, I. G. (1987). Robust empirical Bayes analysis of event rates, Technometrics, 29, 1–15
11	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 DOI
12	Gueorguieva, R. (2001). A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family, Statistical Modelling, 1, 177–193
13	Ha, I. D., Lee, Y. and Song, J.-K. (2001). Hierarchical likelihood approach for frailty models, Biometrika, 88, 233–243
14	Ha, I. D., Lee, Y. and MacKenzie, G. (2007). Model selection for multi-component frailty models, Statistics in Medicine, 26, 4790–4807 DOI ScienceOn
15	Jiang, J. (2007). Linear and generalized linear mixed models and their applications, Springer, New York
16	Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society B, 58, 619–678
17	Barndorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic techniques for use in Statistics, Chapman and Hall, New York