positive loglikelihoods and negative AIC's

[#1]

I 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!

[#2]

You 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,

[#3]

Thanks! 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

[#4]

I 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.

[#5]

Full 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

[#6]

Here 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.

[#7]

Ahh, 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!

[#8 · Accepted solution]

It 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.

[#9]

Hi, 

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. 

[#10]

This was in JMP 10. I think it is different on JMP 14, can check.