The Unobserved Heterogeneity Distribution in Duration Analysis

In a large class of hazard models with proportional unobserved heterogeneity, the distribution of the heterogeneity among survivors converges to a gamma distribution. This convergence is often rapid. We derive this result as a general result for exponential mixtures and explore its implications for the specification and empirical analysis of univariate and multivariate duration models.

[1]  A. Yashin,et al.  What Difference Does the Dependence Between Durations Make? Insights for Population Studies of Aging , 1999, Lifetime data analysis.

[2]  R. Gill,et al.  A simple test for the proportional hazards , 1987 .

[3]  Nancy Brandon Tuma,et al.  Sociological Methodology 1985. , 1987 .

[4]  Gerard J. van den Berg,et al.  Duration models: specification, identification and multiple durations , 2000 .

[5]  Thomas A. Louis,et al.  Time-Dependent Association Measures for Bivariate Survival Distributions , 1992 .

[6]  T. Richards,et al.  Correcting for unmeasured heterogeneity in hazard models using the Heckman-Singer procedure , 1985 .

[7]  Tony Lancaster,et al.  ECONOMETRIC METHODS FOR THE DURATION OF UNEMPLOYMENT , 1979 .

[8]  D. Oakes,et al.  Bivariate survival models induced by frailties , 1989 .

[9]  K Borch-Johnsen,et al.  Heterogeneity models of disease susceptibility, with application to diabetic nephropathy. , 1994, Biometrics.

[10]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[11]  R. Gill,et al.  A simple test of the proportional hazards assumption , 1987 .

[12]  J J Heckman,et al.  Econometric mixture models and more general models for unobservables in duration analysis , 1994, Statistical methods in medical research.

[13]  D. Dabrowska,et al.  Methods for comparing cumulative hazard functions in a semi-proportional hazard model. , 1992, Statistics in medicine.

[14]  R. Gill,et al.  Variance Components Models for Survival DataJ , 1996 .

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

[16]  Kjell A. Doksum,et al.  Graphical comparison of cumulative hazards for two populations , 1989 .

[17]  N. Keiding,et al.  The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates. , 1997, Statistics in medicine.

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

[19]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[20]  Joel L. Horowitz,et al.  Semiparametric Estimation of a Proportional Hazard Model with Unobserved Heterogeneity , 1999 .

[21]  C. McCulloch,et al.  A hazard rate approach to the timing of births. , 1984, Econometrica : journal of the Econometric Society.

[22]  Philip Hougaard,et al.  Measuring the Similarities between the Lifetimes of Adult Danish Twins Born between 1881–1930 , 1992 .

[23]  Stephen Nickell,et al.  Estimating the Probability of Leaving Unemployment , 1979 .

[24]  Thomas Coleman,et al.  Unemployment Behavior Evidence from the CPS Work Experience Survey , 1989 .

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

[26]  Geert Ridder,et al.  Constructive identification of the mixed proportional hazards model , 1995 .

[27]  Susan A. Murphy,et al.  Asymptotic Theory for the Frailty Model , 1995 .

[28]  Related Topics,et al.  Survival analysis : state of the art , 1992 .

[29]  J. Klein,et al.  Estimating Random Effects In the Framingham Heart Study , 1992 .

[30]  L A Lillard,et al.  Simultaneous equations for hazards: marriage duration and fertility timing. , 1993, Journal of econometrics.

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

[32]  Chris Elbers,et al.  True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model , 1982 .

[33]  Testing the hypothesis of proportional hazards in two populations , 1995 .

[34]  Angelo Melino,et al.  Duration dependence and nonparametric heterogeneity: A Monte Carlo study , 2000 .

[35]  Richard D. Gill,et al.  A counting process approach to maximum likelihood estimation in frailty models , 1992 .

[36]  C. Huber-Carol,et al.  Effects of omitting covariates in Cox's model for survival data , 1988 .

[37]  Nancy Flournoy,et al.  Assessment of Dependence In the Life Times of Twins , 1992 .

[38]  Susan A. Murphy,et al.  Consistency in a Proportional Hazards Model Incorporating a Random Effect , 1994 .