------ begin inclusion --------- Dear all, I need to calculate likelihood ratio test for ridge regression. In February I have reported a bug where coxph returns unpenalized log-likelihood for final beta estimates for ridge coxph regression. In high-dimensional settings ridge regression models usually fail for lower values of lambda. As the result of it, in such settings the ridge regressions have higher values of lambda (e.g. over 100) which means that the difference between unpenalized log-likelihood and penalized log-likelihood is not insignificant. I would be grateful if someone can confirm that the below code is correct workaround.
--- end included message ---- First, the "bug" you report is not a bug. The log partial likelihood from a Cox model LPL(beta) is well defined for any vector of coefficients beta, whether they are result of a maximization or taken from your daily horoscope. The loglik component of coxph is the LPL for the reported coefficients. For a ridge regression the coxph function maximizes LPL(beta) - penalty(beta) = penalized partial likelihood = PPL(beta). You have correctly recreated the PPL. Second: how do you do formal tests on such a model? This is hard. The difference LPL1- LPL2 is a chi-square when each is the result of maximizing the Cox LPL over a set of coefficients; when using a PPL we are maximizing over something else. The distribution of the difference of constrained LPL values can be argued to be a weighed sum of squared normals where the weights are in (0,1), which is something more complex than a chisq distribution. In a world with infinite free time I'd have pursued this, worked it all out, and added appropriate code to coxph. What about the difference in PPL values, which is the test you propose? I'm not aware of any theory showing that these have any relation to a chi-square distribution. (Said theory may well exist, and I'd be happy for pointers.) Terry Therneau ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
