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Analysing longitudinal count data with overdispersion

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  • Vandna Jowaheer

Abstract

In many biomedical studies, longitudinal count data comprise repeated responses and a set of multidimensional covariates for a large number of individuals. When the response variable in such models is subject to overdispersion, the overdispersion parameter influences the marginal variance. In such cases, the overdispersion parameter plays a significant role in efficient estimation of the regression parameters. This raises the need for joint estimation of the regression parameters and the overdispersion parameter, the longitudinal correlations being nuisance parameters. In this paper, we develop a generalised estimating equations approach based on a general autocorrelation structure for the repeated overdispersed data. The asymptotic properties of the estimators of the main parameters are discussed, and the estimation methodology is illustrated by analysing data on epileptic seizure counts. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Vandna Jowaheer, 2002. "Analysing longitudinal count data with overdispersion," Biometrika, Biometrika Trust, vol. 89(2), pages 389-399, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:389-399
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    Cited by:

    1. Dimitris Karlis & Naushad Mamode Khan & Yuvraj Sunecher, 2024. "The Negative Binomial INAR(1) Process under Different Thinning Processes: Can We Separate between the Different Models?," Stats, MDPI, vol. 7(3), pages 1-15, July.
    2. Sneddon, Gary & Sutradhar, Brajendra C., 2004. "On semiparametric familial-longitudinal models," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 369-379, September.
    3. N. Mamode Khan & Y. Sunecher & V. Jowaheer & M. M. Ristic & M. Heenaye-Mamode Khan, 2019. "Investigating GQL-based inferential approaches for non-stationary BINAR(1) model under different quantum of over-dispersion with application," Computational Statistics, Springer, vol. 34(3), pages 1275-1313, September.
    4. Brajendra C. Sutradhar & Nan Zheng, 2018. "Inferences in Binary Dynamic Fixed Models in a Semi-parametric Setup," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 263-291, November.
    5. Wan, Wai-Yin & Chan, Jennifer So-Kuen, 2011. "Bayesian analysis of robust Poisson geometric process model using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 687-702, January.
    6. Goncalves, M. Helena & Salome Cabral, M. & Carme Ruiz de Villa, Maria & Escrich, Eduardo & Solanas, Montse, 2007. "Likelihood approach for count data in longitudinal experiments," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6511-6520, August.
    7. Christoph Jeßberger, 2011. "Multilateral Environmental Agreements up to 2050: Are They Sustainable Enough?," ifo Working Paper Series 98, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    8. Brajendra C. Sutradhar & Vandna Jowaheer & R. Prabhakar Rao, 2016. "Semi-Parametric Models for Negative Binomial Panel Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 269-303, August.
    9. Yuvraj Sunecher & Naushad Mamode Khan & Miroslav M. Ristić & Vandna Jowaheer, 2019. "BINAR(1) negative binomial model for bivariate non-stationary time series with different over-dispersion indices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 625-653, December.
    10. Yuvraj Sunecher & Naushad Mamode Khan, 2024. "On Comparing and Assessing Robustness of Some Popular Non-Stationary BINAR(1) Models," JRFM, MDPI, vol. 17(3), pages 1-13, February.
    11. Ye, Fei & Yue, Chen & Yang, Ying, 2013. "Modeling time-dependent overdispersion in longitudinal count data," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 257-264.
    12. Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
    13. Lee, Keunbaik & Joo, Yongsung, 2019. "Marginalized models for longitudinal count data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 47-58.
    14. Alwell J. Oyet & Brajendra C. Sutradhar, 2021. "Analyzing Unevenly Spaced Longitudinal Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 342-373, November.
    15. Miroslav M. Ristić & Yuvraj Sunecher & Naushad Mamode Khan & Vandna Jowaheer, 2019. "A GQL-based inference in non-stationary BINMA(1) time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 969-998, September.
    16. Brajendra C. Sutradhar, 2008. "On forecasting counts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 109-129.
    17. Jowaheer, Vandna, 2006. "Model misspecification effects in clustered count data analysis," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 470-478, March.

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