Abstract
We consider two estimation schemes based on penalized quasilikelihood and quasi-pseudo-likelihood in Poisson mixed models. The asymptotic bias in regression coefficients and variance components estimated by penalized quasilikelihood (PQL) is studied for small values of the variance components. We show the PQL estimators of both regression coefficients and variance components in Poisson mixed models have a smaller order of bias compared to those for binomial data. Unbiased estimating equations based on quasi-pseudo-likelihood are proposed and are shown to yield consistent estimators under some regularity conditions. The finite sample performance of these two methods is compared through a simulation study.
Similar content being viewed by others
References
Breslow NE (1984). Extra-Poisson variation in log-linear models. Appl Statist 33: 38–44
Breslow NE (1990). Tests of hypotheses in overdispersed Poisson regression and other quasi-likelihood models. J Amer Statist Assoc 85: 565–571
Breslow NE and Clayton DG (1993). Approximate inference in generalized linear mixed models. J Amer Statist Assoc 88: 9–25
Breslow NE and Lin X (1995). Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika 82: 81–91
Davidian M and Carroll RJ (1987). Variance function estimation. J Amer Statist Assoc 82: 1079–1091
Green PJ (1987). Penalized likelihood for general semi-parametric regression models. Int Statist Rev 55: 245–259
Gumpertz ML and Pantula SG (1992). Nonlinear regression with variance components. J Amer Statist Assoc 87: 201–209
Heagerty PJ and Lele SR (1998). A composite likelihood approach to binary spatial data. J Amer Statist Assoc 93: 1099–1111
Hinde J (1982) Compound Poisson regression models. In: Gilchrist Berline R (ed) GLIM 82: Proceedings of the International Conference on Generalised Linear Models. Springer-Verlag, pp 109–121
Lawless JF (1987). Negative binomial and mixed Poisson regression. Can J Statist 15: 209–225
Lin X and Breslow NE (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. J Amer Statist Assoc 91: 1007–1016
Liu Q and Pierce DA (1993). Heterogeneity in Mantel-Haenszel-type models. Biometrika 80: 543–556
McCullagh P and Nelder JA (1989). Generalized linear models, 2nd ed. Chapman and Hall, London
Miller JJ (1977). Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance. Ann Statist 5: 746–762
Morton R (1987). A generalized linear model with nested strata of extra-Poisson variation. Biometrika 74: 247–257
Nelder JA and Lee Y (1992). Likelihood, quasi-likelihood and pseudolikelihood: some comparisons. J R Statist Soc B 50: 266–268
Prentice RL and Zhao LP (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47: 825–839
Schall R (1991). Estimation in generalized linear models with random effects. Biometrika 40: 917–927
Solomon PJ and Cox DR (1992). Nonlinear components of variance models. Biometrika 79: 1–11
Stiratelli R, Laird N and Ware J (1984). Random effect models for serial observations with binary response. Biometrics 40: 961–971
Thall PF and Vail SC (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics 46: 657–671
Zeger SL, Liang KY and Albert PS (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics 44: 1049–1060
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lin, X. Estimation using penalized quasilikelihood and quasi-pseudo-likelihood in Poisson mixed models. Lifetime Data Anal 13, 533–544 (2007). https://doi.org/10.1007/s10985-007-9071-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10985-007-9071-z