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I have a model with a likelihood ratio of 1e-6 and yet it spectacularly fails the Osius-Rojek GOF test. How is this possible? It has a nice sigmoidal shape and pretty narrow 95% bounds.

Can I still say "An increase in X correlates to an increase in Y?"

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  • $\begingroup$ I'm not familiar with the test. Did you try Hosmer-Lemeshow? $\endgroup$
    – William Chiu
    Commented Jan 12, 2016 at 16:13
  • $\begingroup$ I was steered away from the HL test due it's erratic behavior and the supposedly arbitrary choice of 10 bins. SOURCE: support.sas.com/resources/papers/proceedings14/1485-2014.pdf $\endgroup$
    – rconway91
    Commented Jan 12, 2016 at 16:21
  • $\begingroup$ @rconway91 you need two models to calculate a likelihood ratio. Can you describe how you calculated it? $\endgroup$
    – AdamO
    Commented Jan 12, 2016 at 16:39
  • $\begingroup$ Some more info: N = 300. Single predictor with continuous data. The likelihood ratio is calculated by: 2*(LogLikeFITTED-LogLikeNULL) which follows a chi2; where the NULL model is the log likelihood of pHat (average rate). I quite confident in my calculation of the likelihood ratio. $\endgroup$
    – rconway91
    Commented Jan 12, 2016 at 16:42

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These tests are telling you different things. The likelihood ratio test (de facto) tells you that the fitted risk in the full model provide better prediction than a model with no predictors. The goodness of fit test tells you that the assumptions underlying the model may be inappropriate, such as whether the fitted risk for the predictors actually follows an S-shape curve.

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  • $\begingroup$ So can I still claim a correlation with no predictive value? $\endgroup$
    – rconway91
    Commented Jan 12, 2016 at 16:49
  • $\begingroup$ @rconway91 I would use robust error estimation and look at the robust confidence interval for the beta coefficient. This ensures that you measure the average effect and can claim correlation with no predictive value as you say. (I wouldn't say "no" predictive value, though) $\endgroup$
    – AdamO
    Commented Jan 12, 2016 at 16:53

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