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Possible Duplicate:
Hosmer-Lemeshow vs AIC: Logistic Regression

To assess the goodness of fit of a model... is the likelihood ratio test better than the H-L test in general?

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Thomas
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  • What kinds of models (logistic, presumably) and which LR tests do you have in mind specifically? – whuber Nov 22 '11 at 17:26
  • @huber: logistic models. Just the LR test with the full versus no variables. – Thomas Nov 22 '11 at 18:07
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    The LR test and the H-L test assess completely different things, though! The LR test merely assesses whether including all the variables does any good at all; the H-L test assesses whether the response (as transformed by the logit link) is approximately a linear function of the variables. – whuber Nov 22 '11 at 19:02
  • @whuber: So if I have a model with a significant L-R test....but the AIC is very low...can I still use it versus another model with a higher AIC but non-significant L-R test? – Thomas Nov 22 '11 at 19:05
  • I'm not aware that AIC has an absolute meaning or that you can compare two different models in that way. – whuber Nov 22 '11 at 19:08
  • @whuber: Models with lower AIC are better than ones with higher AIC. – Thomas Nov 22 '11 at 19:09
  • Not in an unqualified way. There's some discussion elsewhere on this site, such as http://stats.stackexchange.com/questions/577/is-there-any-reason-to-prefer-the-aic-or-bic-over-the-other. One common mistake occurs when some of the regressors have missing values; in this case, the AICs of two models simply aren't comparable. Regardless, AIC is not a goodness of fit measure; it is merely a crude way to assess how much reduction in the log likelihood is achieved by including more parameters. The LR test (for *nested* models) does the same in a better way. – whuber Nov 22 '11 at 19:16
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    @whuber: So what should I do if I have a model with the lowest AIC but significant HL test and another model with non-significant HL test? – Thomas Nov 22 '11 at 19:46
  • Now *that's* an interesting question! Maybe that's the one you would really like to be asking here. An example (perhaps of the output of the two competing models and of the H-L test) might help you get good, targeted responses, too. – whuber Nov 22 '11 at 20:15
  • @whuber: I asked this question here but didn't get a sufficient answer: http://stats.stackexchange.com/questions/18750/hosmer-lemeshow-vs-aic-logistic-regression – Thomas Nov 22 '11 at 22:39
  • You really should just modify that question, then, rather than proliferate a bunch of threads that ask essentially the same thing. – whuber Nov 22 '11 at 22:40

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Regardless of what's better for the sample and model at hand, it's probably better to do both. They work differently, so they'll catch different issues. (I assume you're testing the fit of a logistic regression.)

Thomas Levine
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