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

Yıl 2014, Cilt: 6 Sayı: 1, 24 - 41, 01.04.2014

Mojtaba Ganjali T. Baghfalaki D. Berridge

https://doi.org/10.33818/ier.278029

Öz

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.

Anahtar Kelimeler

Accelerated Failure Time Model, Bayesian Analysis, Interval Censoring, Kaplan-Meier Method, MCMC.

Kaynakça

• Casella, G. and E. I. George (1992). Explaining the Gibbs sampler. The American Statistician, 46 (3), 167–174.
• Campolieti, M. (2001). Bayesian Semiparametric Estimation of Discrete Duration Models: An Application of the Dirichlet Process Prior. Journal of Applied Economics, 16, 1–22.
• Celeux, G., F. Forbes, C. P. Robert and D. M. Titterington (2006). Deviance information criteria for missing data models. Bayesian Anaysis, 1(4), 651–674.
• Cox, D. R. (1972). Regression models and life tables. Journal of Royal Statistical Society B, 34, 187–220.
• DeIorio, M. and C. P. Robert (2002). Discussion of Spiegelhalter et al. Journal of the Royal Statistical Society, Series B, 64, 629–630.
• Deshpande, J. V. and S. G. Purohit (2005). Life Time Data: Statistical Models and Methods. World Scientific, Singapore.
• Duchateau, L., P. Janssen, P. Lindsey, C. Legrand, R. Nguti and R. Sylvester (2002). The shared frailty model and the power for heterogeneity tests in multicenter trials. Computational Statistics and Data Analysis. 40 (3), 603–620.
• Gelman, A. and D. B. Rubin (1992). Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7, 457–511.
• Greene, W. H. (2003). Econometric Analysis. 5th edition, Prentice Hall.
• Hagenaars, J. A. and A. L. McCutcheon (2002). Applied Latent Class Analysis. Cambridge: Cambridge University Press.
• Heckman, J. J. and B. Singer, (1982). Population heterogeneity in demographic models. In Multidimensional Mathematical Demography, ed. K. Land and A. Rogers. New York: Academic.
• Heckman, J. J. and B. Singer (1984). The identifiability of the proportional hazard model. Review of Economic Studies, 51, 231–241.
• Ibrahim, J. G., M. H. Chen and D. Sinha (2002). Bayesian Survival Analysis. Springer- Verlag, New York.
• Knape, J., N. Jonzen, M. Skold, J. Kikkawa and H. McCallum (2011). Individual heterogeneity and senescence in Silvereyes on Heron Island. Ecology, 92, 813–820
• Komarek, A., E. Lesaffre and C. Legrand (2007). Baseline and treatment effect heterogeneity for survival times between centers using a random effects accelerated failure time model with flexible error distribution. Statistics in Medicine, 26, 5457–5472.
• Komarek, A., A. Lesaffre and J. F. Hilton (2005). Accelerated failure time model for arbitrarily censored data with smoothed error distribution. Journal of Computational and Graphical Statistics, 14, 726–745.
• Laird, N. M. and J. H. Ware (1982). Random-effects models for longitudinal data. Biometrics, 38, 963–974.
• Lancaster, T. (1990). The Economic Analysis of Transition Data. Cambridge: Cambridge University Press.
• Lee, E. T. and G. W. Wang (2003). Statistical Methods for Survival Data Analysis. Lifetime Learning Publications. Wiley, New York.
• Legrand, C., V. Ducrocq, P. Janssen, R. Sylvester and L. Duchateau (2005). A Bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model. Statistics in Medicine, 24, 3789–3804.
• Lehmann, E. L. and G. Casella (1998). Theory of Point Estimation. 2nd edition, New York: Springer.
• Omori, Y. and R. A. Johnson (1993). The Influence of Random Effects on the Unconditional Hazard Rate and Survival Function. Biometrika, 80, 910–924.
• Pan, W. and T. A. Louis (2000). A linear mixed-effects model for multivariate censored data. Biometrics, 56, 160–166.
• Spiegelhalter, D. J., N. G. Best, B. P. Carlin and A. Lindevan der (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society-Series B, 64, 583– 616.
• Spiegelhalter. D. J., A. Thomas, N. Best and D. Lunn (2003). WinBUGS Examples, MRC Biostatistics Unit, Institute of Public Health and Department of Epidemiology and Public Health. Imperial College School of Medicine, UK.
• Tempelman, R. J. and D. Gianola (1996). A mixed effects model for overdispersed count data in animal breeding. Biometrics, 52, 265–279.
• Tuma, N. B. and M. T. Hannan (1984). Social Dynamics: Models and Methods. New York: Academic.
• Vaupel, J. W., K. G. Manton and E. Stallard (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–54.
• Vermunt, J. K. (2002). A General Latent Class Approach to Unobserved Heterogeneity in the Analysis of Event History Data. In Applied Latent Class Analysis. 1st ed. Cambridge: Cambridge University Press, 383-407. http://dx.doi.org/10.1017/CBO9780511499531. 015
• Vindenes, Y., S. Engen and B. E. Saether (2008). Individual heterogeneity in vital parameters and demographic stochasticity. American Naturalist, 171, 455–467.
• Wienke, A. (2011). Frailty models in survival analysis. Chapman Hall/CRC.
• Yamaguchi, T. and Y. Ohashi (1999). Investigating centre effects in a multi-centre clinical trial of superficial bladder cancer. Statistics in Medicine, 18, 1961–1971.