positive loglikelihoods and negative AIC'sI noticed that JMP invariably reports positive LLs and negative AICs, for example "-2LL = -1406.88" or "AICc = -1451.534". This does not make sense, does it? LL must be negative by definition; AIC can in principle be negative, but with low LLs and low number of parameters it usually is positive.
Am I missing something fundamental here?
Thanks!
Re: positive loglikelihoods and negative AIC'sPlease do not delete this post. This discuss is useful to other users who might have trouble finding -2L, too.
Re: positive loglikelihoods and negative AIC'sThis was in JMP 10. I think it is different on JMP 14, can check.
Re: positive loglikelihoods and negative AIC'sHi,
Can you please explain where the -2LL are reported? I'm only seeing final AICc values on my end. I'm in JMP 14.
UPDATE: Never mind, I figured it out (I needed to do a GLM) and now I can't figure out how to delete this post.
Re: positive loglikelihoods and negative AIC'sIt is from a MLE procedure. The estimation minimizes -2L.
Yes, you can use twice the difference between the log likelihood under the null and the alternative hypotheses for a LRT chi square test.
Re: positive loglikelihoods and negative AIC'sAhh, got it. This LL is not from a ML procedure. Then my last question: can I still use these values in a log-ratio test or are they not good for that?
Thanks for your help!Re: positive loglikelihoods and negative AIC'sHere is the computation of AICc for a continuous response:
The first term is -2L. So if you have a small SSE (a good fit), then -2L can be negative.
Re: positive loglikelihoods and negative AIC'sFull model -LogLikelihood = -1459.5116. I.e. LogLikelihood = 1459.5116. >0. Cannot be. Either this is not LL, or it is, but there is a minus in there that should not be there.
Or I am missing something big way.
Thanks
Re: positive loglikelihoods and negative AIC'sI don't see anything wrong with these results. If you are concerned about the negative AICc, that happens all the time. There really isn't any scale here. Smaller AICc always suggests a better model. So a model with AICc = 1000 is better than a model with AICc = 1200. A model with AICc = -1250 is better than a model with AICc = -1200.
Re: positive loglikelihoods and negative AIC'sThanks! In the example you give everything is "good". LL negative BIC and AIC positive. So it does not quite answer my question. I see how
So should I assume that this is a type (minus should not be there, see lines marked with >>>>) in a report like this?
Generalized Linear Model Fit
Overdispersion parameter estimated by Maximum Likelihood
Response: O2Cons_ugO2/mgWW
Distribution: Normal
Link: Identity
Estimation Method: Maximum Likelihood
Observations (or Sum Wgts) = 369
Regression Plot
Whole Model Test
>>>>Model -LogLikelihood L-R ChiSquare DF Prob>ChiSq
>>>>Difference 60.566153 121.1323 1 <.0001
>>>>Full -1459.5116
>>>>Reduced -1398.9455
Goodness Of Fit Statistic ChiSquare DF Prob>ChiSq Overdispersion
Pearson 0.0079 367 1.0000 0.0000
Deviance 0.0079 367 1.0000
AICc
-2912.958
Effect Tests
Source DF L-R ChiSquare Prob>ChiSq
assayT 1 121.13231 <.0001
Parameter Estimates
Term Estimate Std Error L-R ChiSquare Prob>ChiSq Lower CL Upper CL
Intercept 0.001544 0.0007616 4.0872942 0.0432 0.0000474 0.0030406
assayT 0.0003546 0.0000296 121.13231 <.0001 0.0002964 0.0004127
Studentized Deviance Residual by Predicted
Re: positive loglikelihoods and negative AIC'sYou may have not seen exceptions but they can happen. You are correct that the log-likelihood is always negative because the likelihood is always 0 to 1. Similarly, the -2L is always positive. AICc, though, can be negative or positive.
For example,
