Discrete state transition models in exploratory research

Abstract

The paper deals with discrete state transition models in the context of exploratory research, where robust methods are required and particular interest lies on covariate coefficients. If there is unobserved heterogeneity, Cox's partial likelihood estimators are inconsistent, and models that completely specify the likelihood, including autocorrelation mechanism of heterogeneity components, are not robust. Separate estimation of likelihood terms regarding spells of different order does not require specification of the autocorrelation pattern among heterogeneity components, but inconsistent estimates are generally produced. Conditions for consistency and efficiency of this method are given. A more robust separate estimation strategy is proposed. It can be applied if the length of the observation period is a random variable independent from the process under study. The application deals with histories of heroin addiction of patients in charge of a public rehabilitation centre, from the beginning of treatment thereon.