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On a Unified Generalized Quasi–likelihood Approach for Familial–Longitudinal Non‐Stationary Count Data

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  • BRAJENDRA C. SUTRADHAR
  • VANDNA JOWAHEER
  • GARY SNEDDON

Abstract

. In this paper, conditional on random family effects, we consider an auto‐regression model for repeated count data and their corresponding time‐dependent covariates, collected from the members of a large number of independent families. The count responses, in such a set up, unconditionally exhibit a non‐stationary familial–longitudinal correlation structure. We then take this two‐way correlation structure into account, and develop a generalized quasilikelihood (GQL) approach for the estimation of the regression effects and the familial correlation index parameter, whereas the longitudinal correlation parameter is estimated by using the well‐known method of moments. The performance of the proposed estimation approach is examined through a simulation study. Some model mis‐specification effects are also studied. The estimation methodology is illustrated by analysing real life healthcare utilization count data collected from 36 families of size four over a period of 4 years.

Suggested Citation

  • Brajendra C. Sutradhar & Vandna Jowaheer & Gary Sneddon, 2008. "On a Unified Generalized Quasi–likelihood Approach for Familial–Longitudinal Non‐Stationary Count Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 597-612, December.
    • Handle: RePEc:bla:scjsta:v:35:y:2008:i:4:p:597-612
    DOI: 10.1111/j.1467-9469.2008.00607.x
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    References listed on IDEAS

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    1. Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
    2. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May.
    3. M. Pourahmadi & M. J. Daniels, 2002. "Dynamic Conditionally Linear Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 58(1), pages 225-231, March.
    4. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    5. Sutradhar, Brajendra C. & Jowaheer, Vandna, 2003. "On familial longitudinal Poisson mixed models with gamma random effects," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 398-412, November.
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