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Dependence Measures in Bivariate Gamma Frailty Models

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  • van den Berg, Gerard J.

    ()
    (University of Mannheim)

  • Effraimidis, Georgios

    ()
    (University of Southern Denmark)

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    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.

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    Bibliographic Info

    Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 8083.

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    Length: 36 pages
    Date of creation: Mar 2014
    Date of revision:
    Handle: RePEc:iza:izadps:dp8083

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    Related research

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

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    1. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. Robin Henderson, 2003. "A serially correlated gamma frailty model for longitudinal count data," Biometrika, Biometrika Trust, vol. 90(2), pages 355-366, June.
    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. David Oakes, 2008. "On consistency of Kendall's tau under censoring," Biometrika, Biometrika Trust, vol. 95(4), pages 997-1001.
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