A flexible model to fit over-dispersed longitudinal count data

References

• Breslow, N. E., and D. G. Clayton. 1993. “Approximate Inference in Generalized Linear Mixed Models.” Journals of the American Statistical Association 88:9–25. doi: 10.2307/2290687.
   Web of Science ®Google Scholar
• Fotouhi, A. R. 2008. “Modelling Overdispersion in Longitudinal Count Data in Clinical Trials with Application to Epileptic Data.” Contemporary Clinical Trials 29 (4):547–554. doi: 10.1016/j.cct.2008.01.005.
   PubMed Web of Science ®Google Scholar
• Gillispie, S. B., and C. G. Green. 2015. “Approximating the Conway-Maxwell-Poisson Distribution Normalizing Constant.” Statistics 49 (5):1062–1073. doi: 10.1080/02331888.2014.896919.
   Web of Science ®Google Scholar
• Grunwald, G. K., S. Bruce, L. Jiang, M. Strand, and N. Rabinovitch. 2011. “A Statistical Model for Under- or Over Dispersed Clustered and Longitudinal Count Data.” Biometrical Journal 53 (4):578–594. doi: 10.1002/bimj.201000076.
   PubMed Web of Science ®Google Scholar
• Hall, D. B., and T. A. Severini. 1998. “Extended Generalized Estimating Equations for Clustered Data.” Journal of the American Statistical Association 93 (444):1365–1375. doi: 10.1080/01621459.1998.10473798.
   Web of Science ®Google Scholar
• Hilbe, J. M., and J. W. Hardin. 2014. “Modeling Count Data with Generalized Distribution.” Stata Journal 14 (3):562–579. doi: 10.1177/1536867X1401400306.
   Web of Science ®Google Scholar
• Jorgensen, B., and S. J. Knudsen. 2004. “Parameter Orthogonality and Bias Adjustment for Estimating Functions.” Scandinavian Journal of Statistics 31 (1):93–114. doi: 10.1111/j.1467-9469.2004.00375.x.
   Web of Science ®Google Scholar
• Jowaheer, V., and N. A. Mamodekhan. 2009. “Estimating Regression Effects in COM-Poisson Generalized Linear Model.” International Journal of Mathematical and Statistical Sciences 1 (2):59–63.
   Google Scholar
• Jowaheer, V., and N. A. Mamodekhan. 2011. “COM-Poisson Model with AR(1)-Type Correlation Structure for Longitudinal Count Response Data.” International Statistical Institute, Proceedings of the 58th World Statistical Congress, Dublin (Session CPS044).
   Google Scholar
• Leppik, I. E., F. E. Dreifuss, T. Bowman, N. Santilli, M. Jacobs, C. Crosby, J. Cloyd, J. Stockman, N. Graves, T. Sutula, T. Welty, J. Vickery, R. Brundage, R. Gumnit and A. Gutierres. 1985. “A Double-blind Crossover Evaluation of Progabide in Partial Seizures”, Neurology 35 (4):285–295.
   Google Scholar
• Liang, k Y., and S. L. Zeger. 1986. “Longitudinal Data Analysis Using Generalized Linear Models.” Biometrika 73 (1):13–22. doi: 10.1093/biomet/73.1.13.
   Web of Science ®Google Scholar
• Morris, D. S., K. F. Sellers, and A. Menger. 2017. “Fitting a Flexible Model for Longitudinal Count Data Using the NLMIXED Procedure.” SAS Paper (202).
   Google Scholar
• Qu, A., and R. Li. 2006. “Quadratic Inference Functions for Varying-Coefficient Models with Longitudinal Data.” Biometrics 62 (2):379–391. doi: 10.1111/j.1541-0420.2005.00490.x.
   PubMed Web of Science ®Google Scholar
• Qu, A., B. G. Lindsay, and B. Li. 2000. “Improving Generalised Estimating Equations Using Quadratic Inference Functions.” Biometrika 87 (4):823–836. doi: 10.1093/biomet/87.4.823.
   Web of Science ®Google Scholar
• Salama, S. F., A. M. Gad, and A. Mousa. 2016. “Modeling Longitudinal Count Data with Missing Values: A Comparative Study.” Academic Journal of Applied Mathematical Sciences, Academic Research Publishing Group 2 (3):19–26.
   Google Scholar
• SAS Institute Inc. 2015. SAS/STAT[textregistered] 14.1 User’s Guide. Cary, NC: SAS Institute Inc.
   Google Scholar
• Sellers, K., and G. Shmueli. 2010. “A Flexible Regression Model for Count Data.” Annals of Applied Statistics 4:943–961.
   Web of Science ®Google Scholar
• Thall, P. F., and S. C. Vail. 1990. “Some Covariance Models for Longitudinal Count Data with over Dispersion.” Biometrics 46 (3):657–671. doi: 10.2307/2532086.
   PubMed Web of Science ®Google Scholar
• Toscas, P. J., and M. J. Faddy. 2003. “Likelihood-Based Analysis of Longitudinal Count Data Using a Generalized Poisson Model.” Statistical Modelling 3 (2):99–108. doi: 10.1191/1471082X03st050oa.
   Web of Science ®Google Scholar
• Xiaomeng, N., and R. C. Hyunkeun. 2019. “Efficient Regression Modeling for Correlated and Over-Dispersed Count Data.” Communications in Statistics - Theory and Methods 48 (24):6005–6018.
   Web of Science ®Google Scholar