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I am trying to find a source that describes the properties of conditional likelihood estimates like those obtained from conditional logistic regression?

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    $\begingroup$ Regarding the title: "MLE estimates" had "estimates" twice in it, so I just spelled the ML part out (since ML is often used for "machine learning"). $\endgroup$ Jun 21, 2016 at 6:43
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    $\begingroup$ I found this paper which discusses the topic. However, I am surprised that I can't find a book which more comprehensively covers the topic. jstor.org/stable/2984535?seq=1#page_scan_tab_contents $\endgroup$
    – DanRoDuq
    Jun 22, 2016 at 3:05

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I think one of the best discussions of conditional logistic regression can be found in Breslow and Day's IARC publication, Chapter 7 on logistic regression for matched sets.

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  • $\begingroup$ I find this book does not really discuss the properties of cmle. $\endgroup$
    – DanRoDuq
    Jun 22, 2016 at 21:36
  • $\begingroup$ @DanRoDuq Have you read chapter 5? Conditional likelihood estimation is, quite simply, specifying probability models for matched sets conditional upon their marginal distributions. Estimators therefore WLOG follow the same distributional properties of ML estimatosr. $\endgroup$
    – AdamO
    Jun 22, 2016 at 22:07
  • $\begingroup$ Hmm I don't think that's the case. For example the paper that I linked to says: "In contrast to the direct m.l.e., the c.m.l.e. will not in general be efficient in the sense that the asymptotic variance is equal to the Cramer-Rao lower bound for un- biased estimators." $\endgroup$
    – DanRoDuq
    Jun 22, 2016 at 22:35
  • $\begingroup$ @DanRoDuq and that's expected, like I said we are conditioning on all the marginal distributions within strata, pretending to know this information, so we borrow no information at all across strata, that's the inherent cause of loss of efficiency. $\endgroup$
    – AdamO
    Jun 22, 2016 at 22:51
  • $\begingroup$ This is exactly what I am trying to understand, but I do not understand it as you just stated it. what do you mean by "all the marginal distributions within strata" and what do you mean by "borrow no information at all across strata"? :) $\endgroup$
    – DanRoDuq
    Jun 22, 2016 at 23:51

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