Dynamic Discrete-Time Duration Models

Discrete{time grouped duration data, with one or multiple types of terminating events, are often observed in social sciences or economics. In this paper we suggest and discuss dynamic models for exible Bayesian nonparametric analysis of such data. These models allow simultaneous incorporation and estimation of baseline hazards and time{varying covariate eeects, without imposing particular parametric forms. Methods for exploring the possibility of time{varying eeects, as for example the impact of nationality or unemployment insurance beneets on the probability of re{employment, have recently gained increasing interest. Our modeling and estimation approach is fully Bayesian and makes use of Markov Chain Monte Carlo (MCMC) simulation techniques. A detailed analysis of unemployment duration data, with full{time job, part{time job and other causes as terminating events, illustrates our methods and shows how they can be used to obtain reened results and interpretations.

[1]  L. Knorr‐Held.  Conditional Prior Proposals in Dynamic Models , 1999 .

[2]  A. Raftery,et al.  Estimating Bayes Factors via Posterior Simulation with the Laplace—Metropolis Estimator , 1997 .

[3]  Ludwig Fahrmeir,et al.  Smoothing Hazard Functions and Time-Varying Effects in Discrete Duration and Competing Risks Models , 1996 .

[4]  Cristiana Larizza,et al.  A Unified Approach for Modeling Longitudinal and Failure Time Data, With Application in Medical Monitoring , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Alan E. Gelfand,et al.  Model Determination using sampling-based methods , 1996 .

[6]  David J. Spiegelhalter,et al.  Introducing Markov chain Monte Carlo , 1995 .

[7]  J. Besag,et al.  On conditional and intrinsic autoregressions , 1995 .

[8]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[9]  Elja Arjas,et al.  Assessing the Losses Caused by an Industrial Intervention: A Hierarchical Bayesian Approach , 1995 .

[10]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[11]  L. Knorr‐Held.  Markov Chain Monte Carlo Simulation in Dynamic Generalized Linear Mixed Models , 1995 .

[12]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[13]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[14]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[15]  Ludwig Fahrmeir,et al.  Dynamic modelling and penalized likelihood estimation for discrete time survival data , 1994 .

[16]  D Clayton,et al.  Bayesian analysis of survival on multiple time scales. , 1994, Statistics in medicine.

[17]  S. Frühwirth-Schnatter.  Data Augmentation and Dynamic Linear Models , 1994 .

[18]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[19]  O. Aalen,et al.  Further results on the non-parametric linear regression model in survival analysis. , 1993, Statistics in medicine.

[20]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[21]  K. Yamaguchi.  Modeling Time-Varying Effects of Covariates in Event-History Analysis Using Statistics from the Saturated Hazard Rate Model , 1993 .

[22]  D. Hill,et al.  Competing hazards with shared unmeasured risk factors. , 1993, Sociological methodology.

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

[24]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[25]  D G Clayton,et al.  A Monte Carlo method for Bayesian inference in frailty models. , 1991, Biometrics.

[26]  D. Gamerman.  Dynamic Bayesian Models for Survival Data , 1991 .

[27]  Ian W. McKeague,et al.  Weighted Least Squares Estimation for Aalen's Additive Risk Model , 1991 .

[28]  A. Raftery,et al.  Stopping the Gibbs Sampler,the Use of Morphology,and Other Issues in Spatial Statistics (Bayesian image restoration,with two applications in spatial statistics) -- (Discussion) , 1991 .

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

[30]  Mark B. Stewart,et al.  Modelling the Probability of Leaving Unemployment: Competing Risks Models with Flexible Baseline Hazards , 1993 .

[31]  O. Aalen.  A linear regression model for the analysis of life times. , 1989, Statistics in medicine.

[32]  Gerhard Tutz,et al.  Diskrete Modelle zur Analyse von Verweildauer und Lebenszeiten , 1989 .

[33]  Bruce D. Meyer.  Unemployment Insurance and Unemployment Spells , 1988 .

[34]  M. West,et al.  An application of dynamic survival models in unemployment studies , 1987 .

[35]  Elja Arjas,et al.  A logistic regression model for hazard: asymptotic results , 1987 .

[36]  J. Heckman,et al.  Econometric duration analysis , 1984 .

[37]  P. Allison.  Discrete-Time Methods for the Analysis of Event Histories , 1982 .

[38]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

[39]  W. A. Thompson,et al.  On the treatment of grouped observations in life studies. , 1977, Biometrics.

[40]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[41]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .