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Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects

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Abstract

In survival analysis, Cox's name is associated with the partial likelihood technique that allows consistent estimation of proportional hazard scale parameters without specifying a duration dependence baseline. In discrete choice analysis, McFadden's name is associated with the generalized extreme-value (GEV) class of logistic choice models that relax the independence of irrelevant alternatives assumption. This paper shows that the mixed class of proportional hazard specifications allowing consistent estimation of scale and mixing parameters using partial likelihood is isomorphic to the GEV class. Independent censoring is allowed and I discuss approximations to the partial likelihood in the presence of ties. Finally, the partial likelihood score vector can be used to construct log-rank tests that do not require the independence of observations involved.

Suggested Citation

  • Jan Ondrich, 2005. "Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects," Center for Policy Research Working Papers 68, Center for Policy Research, Maxwell School, Syracuse University.
  • Handle: RePEc:max:cprwps:68
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    References listed on IDEAS

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    1. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    2. Hausman, Jerry & McFadden, Daniel, 1984. "Specification Tests for the Multinomial Logit Model," Econometrica, Econometric Society, vol. 52(5), pages 1219-1240, September.
    3. H C W L Williams, 1977. "On the formation of travel demand models and economic evaluation measures of user benefit," Environment and Planning A, Pion Ltd, London, vol. 9(3), pages 285-344, March.
    4. Ridder, Geert & Tunali, Insan, 1999. "Stratified partial likelihood estimation," Journal of Econometrics, Elsevier, vol. 92(2), pages 193-232, October.
    5. H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, , vol. 9(3), pages 285-344, March.
    6. McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
    7. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
    8. Small, Kenneth A & Hsiao, Cheng, 1985. "Multinomial Logit Specification Tests," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 619-627, October.
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    More about this item

    Keywords

    proportional hazard; random effects; partial likelihood; GEV class;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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