The Analysis of Panel Data with a Flexible Frailty

Analysis of panel data under the non-homogeneous Poisson mixed process is investigated. The ordinary Poisson process model is not suitable for the analysis of count data in the presence of overdispersion. For handling the overdispersion problem, a multiplicative finite mixture of gamma distributed random effects is assigned to each individual in the model which gives a non-homogeneous Poisson mixed model. The parameter of the mixed Poisson process (baseline intensity function) is modeled by using psplines and the parameters of the model are estimated by means of the iterative Expectation-Maximization (EM) algorithm. The statistical properties of the proposed count model are investigated through simulation study and the model is used to analyze the Cherry Bark Tortrix Moth data.