Simulated maximum likelihood estimation in transition models

In this paper we analyse the problem of modelling individual transitions in the presence of an incomplete sampling scheme. This problem is particularly cumbersome when a continuous time-scale is used for the modelling and when the model incorporates unobserved heterogeneity. This problem arises, for instance, when the observation is made at fixed time points or stops on an interval of time. In order to take this phenomenon into account, we propose to maximize the simulated likelihood using an importance function. The method can be applied to general continuous-time discrete-state-space processes and a broad class of incomplete sampling schemes.