Estimating Transition Probabilities from Aggregate Samples Augmented by Haphazard Recaptures II. The Case of Covariates.

Abstract

**Please note that the full text is embargoed** ABSTRACT: The paper extends the authors' earlier methods for estimating transition probabilities, by combining aggregate and haphazard recapture data, to the case of categorical covariates. Both fixed and time-dependent covariates are considered. A two-stage estimation procedure is proposed. The first stage uses a Markov model to estimate multivariate transition probabilities for the response and all covariates. The second stage uses the Stage 1 estimates to model covariate effects. The required number of sampling waves depends only on the number of response levels and time-dependent covariate levels — and not on the number of fixed covariate levels. Recommendations are given for the required sampling fraction — which decreases with the increasing population size — to obtain reliable results. A key improvement over the earlier work is the capability to estimate transition probabilities within small strata obtained by post-stratification of a large sample, without requiring the strata sample sizes to be large.