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Is the likelihood ratio test ($-2 \log L$) basically like the partial F-test in that you are using it for logistic regression instead of linear regression?

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For logistic regression you use the asymptotic distribution of the log of likelihood ratio test statistic for variable selection (testing hypotheses or model selection). In the case of linear regression, due to the assumed normality for the error distribution, there is no need to use asymptotics, and the likelihood ratio test static trivially reduces to a ratio of chi-squares, that is, F-distribution.

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  • $\begingroup$ ...and the likelihood ratio test statistic trivially reduces to (through a nonlinear transformation) a ratio of chi-squares... :) (Note also that static should be statistic) :) $\endgroup$ – cardinal Nov 13 '11 at 23:20
  • $\begingroup$ Also, this is very (!) picky, but the $F$-distribution is, as I know you know, not quite a ratio of (independent) chi-squared random variables. :) $\endgroup$ – cardinal Nov 13 '11 at 23:21

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