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Dependence Measures in Bivariate Gamma Frailty Models

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  • van den Berg, Gerard J.

    () (University of Bristol)

  • Effraimidis, Georgios

    () (University of Southern Denmark)

Abstract

Bivariate duration data frequently arise in economics, biostatistics and other areas. In "bivariate frailty models", dependence between the frailties (i.e., unobserved determinants) induces dependence between the durations. Using notions of quadrant dependence, we study restrictions that this imposes on the implied dependence of the durations, if the frailty terms act multiplicatively on the corresponding hazard rates. Marginal frailty distributions are often taken to be gamma distributions. For such cases we calculate general bounds for two association measures, Pearson's correlation coefficient and Kendall's tau. The results are employed to compare the flexibility of specific families of bivariate gamma frailty distributions.

Suggested Citation

  • van den Berg, Gerard J. & Effraimidis, Georgios, 2014. "Dependence Measures in Bivariate Gamma Frailty Models," IZA Discussion Papers 8083, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp8083
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    References listed on IDEAS

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    1. Robin Henderson, 2003. "A serially correlated gamma frailty model for longitudinal count data," Biometrika, Biometrika Trust, vol. 90(2), pages 355-366, June.
    2. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    3. David Oakes, 2008. "On consistency of Kendall's tau under censoring," Biometrika, Biometrika Trust, vol. 95(4), pages 997-1001.
    4. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    5. van den Berg, Gerard J., 1997. "Association measures for durations in bivariate hazard rate models," Journal of Econometrics, Elsevier, vol. 79(2), pages 221-245, August.
    6. Zhong Xiaoyun & Li Hongzhe, 2002. "An additive genetic gamma frailty model for two-locus linkage analysis using sibship age of onset data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 1(1), pages 1-26, November.
    7. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    8. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
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    More about this item

    Keywords

    bivariate gamma distribution; duration models; competing risks; Kendall's tau; negative and positive quadrant dependence; Pearson's correlation coefficient; unobserved heterogeneity; survival analysis;

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

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