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Variance component models for longitudinal count data with baseline information: epilepsy data revisited

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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.

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References

  • Aitkin M. 1999. A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55: 117–128.

    Article  MATH  MathSciNet  Google Scholar 

  • Aitkin M. and Alfó A. M. 2003. Random effect AR models for longitudinal binary responses. Statistical Modelling 3: 291–303.

    Article  MathSciNet  Google Scholar 

  • Alfó M. and Trovato G. 2004. Semiparametric mixture models for multivariate count data, with application. Econometrics Journal 7: 426–454.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Booth J., Casella G., Friedl H., and Hobert J. 2003. Negative binomial loglinear mixed models. Statistical Modelling 3: 179–191.

    Article  MathSciNet  Google Scholar 

  • Breslow N. and Clayton D. 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88: 9–24.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Davidson R. and Mackinnon J. 1993. Estimation and Inference in Econometrics. Oxford University Press, Oxford.

    Google Scholar 

  • Diggle P., Heagerty P., Liang K., and Zeger S. 2003. Analysis of Longitudinal Data, 2nd edition. Oxford University Press, Oxford.

    Google Scholar 

  • Leppik I., Dreifuss F., Porter R., etal. 1987. A controlled study of progabide in partial seizures: methodology and results. Neurology 37: 963–968.

    Google Scholar 

  • Lindsay, B. 1983a. The geometry of mixture likelihoods: a general theory. Annals of Statistics 11: 86–94.

    MathSciNet  Google Scholar 

  • Lindsay, B. 1983b. The geometry of mixture likelihoods, part II: The exponential family. Annals of Statistics 11: 783–792.

    MathSciNet  Google Scholar 

  • Lindsay, B. and Lesperance M. 1995. A review of semiparametric mixture models. Journal of statistical planning and inference 47: 29–39.

    Article  MathSciNet  Google Scholar 

  • Liu, Q. and Pierce D. 1994. A note on Gaussian-Hermite quadrature. Biometrika 81: 624–629.

    Article  MathSciNet  Google Scholar 

  • McLachlan, G. and Peel D. 2000. Finite Mixture Models. John Wiley & Sons, New York.

    Google Scholar 

  • Rabe-Hesketh S., Skrondal A., and Pickles A. 2002. Estimation of generalized linear mixed models. The STATA Journal 2: 1–21.

    Google Scholar 

  • Thall P. and Vail S. 1990. Some covariance models for longitudinal count data with overdispersion. Biometrics 46: 657–671.

    MathSciNet  Google Scholar 

  • Toscas J. and Faddy M. 2003. Likelihood-based analysis of longitudinal count data using a generalized Poisson model. Statistical Modelling 3: 99–108.

    Article  MathSciNet  Google Scholar 

  • Wang P., Puterman M., Cockburn I., and Le N. 1996. Mixed Poisson regression models with covariate dependent rates. Biometrics 52: 381–400.

    Google Scholar 

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Correspondence to Marco Alfò.

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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

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  • DOI: https://doi.org/10.1007/s11222-006-7072-5

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