[R] Question about BIC of two different regression models? how should we compare two regression models?

[John Sorkin]

I believe when using BIC one needs to compare nested models, i.e. , when comparing models A and B one must make sure that model A contains all the parameters of model B and additionally A contains one or more extra parameter beyond those in B. Further the comparison of BICs requires that models A and B be run on the same data. Thus if we have model A  y=age+sex, model B y=age, if some subjects are missing data on their sex, model A would be run on a subset of the data used when running model B. In this case the comparison of BICs would not be valid.
John 

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

>>> Ben Bolker <bbolker at gmail.com> 9/2/2011 2:35 AM >>>
Andra Isan <andra_isan <at> yahoo.com> writes:

> 
> Hi All, 
> In order to compare two different logistic regressions, 
> I think I need to compare them based on their BIC
> values, but I am not sure if the smaller BIC would mean a better 
> model or the reverse is true?
> Thanks a lot,Andra

  Smaller (i.e. lower value) BIC is always better 
(even if BIC happens to be negative, as can happen in some cases; 
i.e. BIC=-1002 is better than BIC=-1000, BIC=1000 is better than BIC=1002).

  I would suggest however that (a) there are better venues for this
question (e.g. stats.stackexchange.com), since it's a stats and not
an R question; (b) it might be a good idea to review a stats text,
or even http://en.wikipedia.org/wiki/Bayesian_information_criterion ,
since this is a pretty basic question.

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