Estimating random effects in a finite Markov chain with absorbing states: Application to cognitive data

Finite Markov chains with absorbing states are popular tools for analyzing longitudinal data with categorical responses. The one step transition probabilities can be defined in terms of fixed and random effects but it is difficult to estimate these effects due to many unknown parameters. In this article we propose a three-step estimation method. In the first step the fixed effects are estimated by using a marginal likelihood function, in the second step the random effects are estimated after substituting the estimated fixed effects into a joint likelihood function defined as a h-likelihood, and in the third step the covariance matrix for the vector of random effects is estimated using the Hessian matrix for this likelihood function. An application involving an analysis of longitudinal cognitive data is used to illustrate the method.