Modelling Longitudinal Discrete Data Affected By One Way Multi-dimensional Random Effects

Abstract: In many economic sectors it is common to collect discrete (such as binary or count) responses along with covariates, from a large number of firms, successively over a small period of time. It may, however, happen in practice that the repeated responses are also affected by firm specific one-way multi-dimensional random effects. Moreover, all the firms under consideration may not be homogeneous, although they may be divided into a small number of homogeneous groups. In this paper, we develop a model to fit such repeated discrete data which are also affected by one-way multi-dimensional heteroscedastic random effects. For the estimation of the regression effects of the model, we use the so-called generalized quasilikelihood (GQL) approach, after taking the heteroscedastic nature of the multi- dimensional variance components (of the random effects) as well as the longitudinal corre-lations of the repeated responses, into account. The proposed GQL estimators are consistent and asymptotically normal