Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects
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.
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- D. McFadden & J. Hausman, 1981.
"Specification Tests for the Multinominal Logit Model,"
292, Massachusetts Institute of Technology (MIT), Department of Economics.
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- Meyer, Bruce D, 1990.
"Unemployment Insurance and Unemployment Spells,"
Econometric Society, vol. 58(4), pages 757-82, July.
- Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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 619-27, October.
- Ridder, G. & Tunali, I., 1997.
"Stratified Partial Likelihood Estimation,"
1997/17, Koc University.
- McFadden, Daniel, 1987. "Regression-based specification tests for the multinomial logit model," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 63-82.
- H C W L Williams, 1977. "On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit," Environment and Planning A, SAGE Publishing, vol. 9(3), pages 285-344, March.
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