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

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  • Jan Ondrich

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," Discussion Papers of DIW Berlin 520, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp520
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    References listed on IDEAS

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    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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