Generalized quasi-likelihood estimation procedure for non-stationary over-dispersed longitudinal counts

Abstract

Poisson log-linear regression model is commonly used for analysing count data. Valid inference based on this model can be drawn when the mean and variance of the data are equal. However, in practice variance of responses is often much greater than the mean of the responses, known as over-dispersion. Also, non-stationarity, i.e. non-constant mean, or/and non-constant variance, and/or covariance that is not solely the function of elapsed time between responses over the period of study, is another issue in the longitudinal study. It has been found that ignoring such departures may arise bias and provide misleading conclusions. As a remedy, negative binomial (NB) regression was suggested by the researcher for modelling longitudinal count. For longitudinal non-stationary count with over-dispersion, there is no established observation-driven model in the literature. Although there exists a non-stationary NB type model in the time series context, this type of observation-driven model has never been used in longitudinal data. In this paper, we have extended the non-stationary model to the longitudinal set-up and proposed a GQL estimation procedure for estimating regression parameters. An extensive simulation study has been carried out through which it has been shown that GQL provides unbiased estimates of the regression parameters. Performance of the method of moment approach for estimating correlation and over-dispersion parameter has also found to be consistent. The proposed model and estimation technique, thereafter, was applied to analyse longitudinal epileptic seizure count data.