Com-Poisson Model with AR(1)-Type Correlation Structure for Longitudinal Count Response Data
Vandna Jowaheer¹, Naushad Ali Mamode Khan²
¹Faculty of Science, University of Mauritius, Reduit, Mauritius; ²Faculty of Social Studies & Humanities, University of Mauritius, Reduit, Mauritius

Analysis of longitudinal count response data, affected by one or more explanatory variables, requires adequate modelling of the correlations underlying the responses repeatedly collected over time. These correlation structures are then used with the corresponding means and variances of the process to formulate quasi-likelihood estimating equations which can be solved to obtain reliable estimates of the regression parameters. True Gaussian ARMA-type correlation structures have been found to be more efficient against 'working' as well as 'random effects based' correlation structures in analysing Poisson longitudinal counts. Quite often, count responses are under-dispersed or over-dispersed relative to Poisson distribution. Com-Poisson distribution, due to its convincing properties, has been widely used to describe under- or over- dispersed count data in cross-sectional set-up. However, there exists no application of Com-Poisson model in longitudinal case. The challenge lies in modelling the correlation structure of repeated Com-Poisson counts. In this paper, we provide the framework for developing a Com-Poisson model with AR(1)-type correlation structure under the longitudinal set-up. We further apply this model to simulated data and obtain the estimates of the regression parameters by solving quasi-likelihood estimating equations.

1. Jowaheer, V. and Sutradhar, B. C. (2002). Analysing longitudinal count data with overdispersion. Biometrika 89, 389-399.

2. Jowaheer, V. and Mamode Khan, N. (2009). Estimating regression effects in Com-Poisson generalised linear model. International Journal of Computational and Mathematical Science 3, 1339-1351.

3. Shmueli, G., Minka, T. P., Kadane, J., Borle, S. and Boatwright, P. (2005). A useful distribution for fitting discrete data: Revival of the Com-Poisson. Applied Statistics: Journal of Royal Statistical Society, series C., 54(1), 127-142.

4. Sutradhar, B. C. (2003). An overview on regression models for discrete longitudinal responses. Statistical Science 18(3), 377-393.

5. Sutradhar, B. C. and Das, K. (1999). On the efficiency of regression estimators in generalised linear models for longitudinal data, Biometrika 86, 459-465.

Keywords: Longitudinal count responses; Over- and under-dispersion; Com-Poisson distribution; Quasi-likelihood estimation

Biography: Dr. Vandna Jowaheer is an Associate Professor in Statistics at the Faculty of Science, University of Mauritius.

Her research expertise lies in designing linear and generalized linear mixed models for clustered, longitudinal and time series data; developing estimation techniques and applying statistical models and methods to analyse socio-economic, environmental and bio-medical data.