A Bayesian Analysis of Unobserved Heterogeneity for Unemployment Duration Data in the Presence of Interval Censoring

In this paper, we discuss Bayesian inference of unobserved heterogeneity for unemployment duration data in the presence of right and interval-censoring, and non-proportionality. We employ accelerated failure time models with three different distributional assumptions: log-logistic, log-normal, and Weibull models, and use members of an exponential family of distributions for considering unobserved heterogeneity. We adopt a Bayesian approach, using Markov Chain Monte Carlo via WinBUGS software, to analyze the data. The proposed approach is illustrated using the unemployment duration data set of Iran in 2009. A sensitivity analysis using different latent variable models of the exponential family is also considered. After checking convergence, using the Gelman-Rubin diagnostic test, we compared different distributional assumptions using the DIC3 criterion. Our findings reveal significant discrepancies in unemployment duration based on different covariates for the sample population of Iran in 2009.