For some given data, suppose I fit two models whose p-values are above 0.1. However, 2 times the negative of likelihood ratio statistic, say L (which asymptotically follows chi-square distribution) are different for the models. Can I say that the model with the minimum L value provides a better fit to the given data ?
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$\begingroup$ You can make a decision on likelihood alone only if both model have the same (or really close) number of parameters otherwise you tend to have a higher likelihood the more parameters you have (and end up with an overfit). That is why you generally use Likelihood Ratio Test to see if the performance of the model is due to few good predictors or a whole bunch of mediocre ones $\endgroup$– RiffCommented May 15, 2017 at 11:47
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$\begingroup$ Why do the p-values matter in your question? What p-values are they (likelihood ratio test versus a null model??)? Why do you wish to say that one model provides a better fit? $\endgroup$– BjörnCommented May 15, 2017 at 12:47
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$\begingroup$ I have a collection of candidate models, which are the null models and a perfect fit model, which is the alternative model. I wish to test which null model provides the best fit to the given data. So, I'm using values of the likelihood ratio test statistic and the corresponding p-values for testing the above hypotheses. $\endgroup$– user143487Commented May 15, 2017 at 13:45
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