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.

[1]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[2]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[3]  J. Heckman,et al.  Population heterogeneity in demographic models. , 1982 .

[4]  J. Heckman,et al.  The Identifiability of the Proportional Hazard Model , 1984 .

[5]  M. Hannan,et al.  Social Dynamics: Models and Methods. , 1986 .

[6]  Tony Lancaster,et al.  The Econometric Analysis of Transition Data. , 1992 .

[7]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[8]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[9]  Richard A. Johnson,et al.  The influence of random effects on the unconditional hazard rate and survival functions , 1993 .

[10]  D. Gianola,et al.  A mixed effects model for overdispersed count data in animal breeding , 1996 .

[11]  T. Yamaguchi,et al.  Investigating centre effects in a multi-centre clinical trial of superficial bladder cancer. , 1999, Statistics in medicine.

[12]  T. Louis,et al.  A Linear Mixed‐Effects Model for Multivariate Censored Data , 2000, Biometrics.

[13]  M. Campolieti.  Bayesian semiparametric estimation of discrete duration models: an application of the dirichlet process prior , 2001 .

[14]  Aki Vehtari.  Discussion to "Bayesian measures of model complexity and fit" by Spiegelhalter, D.J., Best, N.G., Carlin, B.P., and van der Linde, A. , 2002 .

[15]  Catherine Legrand,et al.  The shared frailty model and the power for heterogeneity tests in multicenter trials , 2002 .

[16]  J. Vermunt.  A general latent class approach to unobserved heterogeneity in the analysis of event history data , 2002 .

[17]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[18]  J. Hagenaars,et al.  Applied Latent Class Analysis , 2003 .

[19]  Elisa Lee,et al.  Statistical Methods for Survival Data Analysis: Lee/Survival Data Analysis , 2003 .

[20]  Joseph G. Ibrahim,et al.  Bayesian Survival Analysis , 2004 .

[21]  P. Janssen,et al.  A Bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model , 2005, Statistics in medicine.

[22]  E. Lesaffre,et al.  Accelerated Failure Time Model for Arbitrarily Censored Data With Smoothed Error Distribution , 2005 .

[23]  Jayant V. Deshpande,et al.  Lifetime Data: Statistical Models and Methods , 2006 .

[24]  C. Robert,et al.  Deviance information criteria for missing data models , 2006 .

[25]  Jayant V. Deshpande,et al.  Life-Time Data - Statistical Models and Methods , 2006, Series on Quality, Reliability and Engineering Statistics.

[26]  Catherine Legrand,et al.  Baseline and treatment effect heterogeneity for survival times between centers using a random effects accelerated failure time model with flexible error distribution , 2007, Statistics in medicine.

[27]  Tim B. Swartz,et al.  Bayesian Analysis of Dyadic Data , 2007 .

[28]  S. Engen,et al.  Individual Heterogeneity in Vital Parameters and Demographic Stochasticity , 2008, The American Naturalist.

[29]  W. Greene,et al.  计量经济分析 = Econometric analysis , 2009 .

[30]  J. Vaupel,et al.  The impact of heterogeneity in individual frailty on the dynamics of mortality , 1979, Demography.

[31]  A. Wienke.  Frailty Models in Survival Analysis , 2010 .

[32]  M. Sköld,et al.  Individual heterogeneity and senescence in silvereyes on Heron Island. , 2011, Ecology.

[33]  D.,et al.  Regression Models and Life-Tables , 2022 .