I know I can only use the log-likelihoods of two models as selection criterion if they are nested. However, I don't understand this completely. Why isn't it possible to apply this reasoning to non-nested models? I think the higher the log-likelihood the better fits the model the data. I am also aware of other criteria as AIC but this doesn't helps me to understand the issue with the log-likelihoods.


You can compare the log-likelihoods of two non-nested models. See Cox (1961), "Tests of separate families of hypotheses"), Proc. Fourth Berkeley Symp. on Math. Statist. and Prob., 1 & Cox (1962), "Further results on tests of separate families of hypotheses", JRSS B, 24, 2. But the log-likelihood ratio test statistic doesn't have the asymptotic chi-square distribution with degrees of freedom equal to the difference in the no. estimated parameters that is so convenient when the models compared are nested. See Wilks (1938), "The large-sample distribution of the likelihood ratio for testing composite hypotheses", Ann. Math. Statist., 9, 1.

| cite | improve this answer | |
  • 1
    $\begingroup$ If it is comparable, what is needed to be sure to conclude one model is superior? $\endgroup$ – random_guy Feb 13 '15 at 13:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.