The initial conditions problem in longitudinal count process: A simulation study

In this paper we report some simulation studies to compare two basic approaches in modelling the random effects for longitudinal count data. The first, the naive approach, treats the endogenous initial conditions as exogenous and the second, correct approach, models the initial conditions as endogenous. The initial conditions problem in longitudinal count data arises when the process has a Markov property. In some applications, such as clinical studies, the baseline is used as a covariate. This also creates an initial condition problem even if the process has no Markov property. In this paper we shall consider both types of initial conditions. To see the effect of the error variance, baseline effect and lagged effect different values for these parameters are considered. We will apply the proposed approach to epileptic data and show that ignoring the initial conditions results in exaggerated treatment effect and misleading interpretation for the baseline effect.