Re: Non-Nested Models-model selection

["Barlas, Suna" <suna_barlas@merck.com>]

It does not sound, without further info on what you are trying to do, like you are interested in "model selection" but rather "hypothesis testing" situation. If it was model selection, one could use the usual model selection criteria. But if you are interested in hypothesis testing there are different ways of doing doing it for non-nested models. And as you said, since the models are not nested, the usual LR test statistic will not have an asymptotic Chi-square distribution and hence the statistic you compute will not have a meaningful interpretation. One way to deal with such problems is to embed the two models in a larger model and test significance of the parameter you are interested in testing. You can find related papers in econometric literature. If my memory serves me right, Pesaran, McKinnon and Davidson (?) worked on this problem. If you want to treat the two model on equal footing or you are worried about multi-collinearity, then you may want to modify the LRT test in such a way that it is interpretable - the way D. R. Cox did in his 70's papers on tests of non-nested models. I have used Cox's method several times and it seems to be working pretty well - you just need to do some programming yourself, which can easily be done in S-Plus.

 

Hope this helps ....

Suna Barlas, Ph.D.
Merck & Co., Inc.
WP39-168, P.O. Box 4
West Point, PA 19486-0004
suna_barlas@merck.com

-----Original Message-----
From: s-news-owner@lists.biostat.wustl.edu [mailto:s-news-owner@lists.biostat.wustl.edu] On Behalf Of Pravin
Sent: Wednesday, March 24, 2004 5:17 PM
To: s-news@wubios.wustl.edu
Subject: [S] Non-Nested Models-model selection

Hi all,

Could you please suggest references or relevant links for model selection metric(s) that can be used while dealing with non-nested models:-

For simplicity, I have two competing models:
Model A- Y~intecept+ (alpha+beta*covariate)*time
Model B- Y~intercept+beta*covariate+alpha*time
In a nutshell, I am testing if covariate is affecting the slope or the intercept. As I understand this, the likelihood ratio statistic will not be asymptotically distributed as a chi-square random variable. So it is not a straightforward comparison using likelihood ratio. Please share some of your experiences and different approaches.

Thank you in anticipation,

Pravin

Pravin Jadhav

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