Abstract
Random effect models have often been used in longitudinal data analysis since they allow for association among repeated measurements due to unobserved heterogeneity. Various approaches have been proposed to extend mixed models for repeated count data to include dependence on baseline counts. Dependence between baseline counts and individual-specific random effects result in a complex form of the (conditional) likelihood. An approximate solution can be achieved ignoring this dependence, but this approach could result in biased parameter estimates and in wrong inferences. We propose a computationally feasible approach to overcome this problem, leaving the random effect distribution unspecified. In this context, we show how the EM algorithm for nonparametric maximum likelihood (NPML) can be extended to deal with dependence of repeated measures on baseline counts.
Similar content being viewed by others
References
Aitkin M. 1999. A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55: 117–128.
Aitkin M. and Alfó A. M. 2003. Random effect AR models for longitudinal binary responses. Statistical Modelling 3: 291–303.
Alfó M. and Trovato G. 2004. Semiparametric mixture models for multivariate count data, with application. Econometrics Journal 7: 426–454.
Biernacki C., Celeux G., and Govaert G. 2003. Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models. Computational Statistics and Data Analysis 41: 561–575.
Booth J., Casella G., Friedl H., and Hobert J. 2003. Negative binomial loglinear mixed models. Statistical Modelling 3: 179–191.
Breslow N. and Clayton D. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 9–24.
Crouchley R. and Davies R. B. 1999. A comparison of population average and random effect models for the analysis of longitudinal count data with baseline information. Journal of the Royal Statistical Society, A 162: 331–347.
Davidson R. and Mackinnon J. 1993. Estimation and Inference in Econometrics. Oxford University Press, Oxford.
Diggle P., Heagerty P., Liang K., and Zeger S. 2003. Analysis of Longitudinal Data, 2nd edition. Oxford University Press, Oxford.
Leppik I., Dreifuss F., Porter R., etal. 1987. A controlled study of progabide in partial seizures: methodology and results. Neurology 37: 963–968.
Lindsay, B. 1983a. The geometry of mixture likelihoods: a general theory. Annals of Statistics 11: 86–94.
Lindsay, B. 1983b. The geometry of mixture likelihoods, part II: The exponential family. Annals of Statistics 11: 783–792.
Lindsay, B. and Lesperance M. 1995. A review of semiparametric mixture models. Journal of statistical planning and inference 47: 29–39.
Liu, Q. and Pierce D. 1994. A note on Gaussian-Hermite quadrature. Biometrika 81: 624–629.
McLachlan, G. and Peel D. 2000. Finite Mixture Models. John Wiley & Sons, New York.
Rabe-Hesketh S., Skrondal A., and Pickles A. 2002. Estimation of generalized linear mixed models. The STATA Journal 2: 1–21.
Thall P. and Vail S. 1990. Some covariance models for longitudinal count data with overdispersion. Biometrics 46: 657–671.
Toscas J. and Faddy M. 2003. Likelihood-based analysis of longitudinal count data using a generalized Poisson model. Statistical Modelling 3: 99–108.
Wang P., Puterman M., Cockburn I., and Le N. 1996. Mixed Poisson regression models with covariate dependent rates. Biometrics 52: 381–400.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alfò, M., Aitkin, M. Variance component models for longitudinal count data with baseline information: epilepsy data revisited. Stat Comput 16, 231–238 (2006). https://doi.org/10.1007/s11222-006-7072-5
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11222-006-7072-5