Date:         Thu, 16 Jun 2005 12:24:16 -0700
Reply-To:     Vadim Pliner <Vadim.Pliner@VERIZONWIRELESS.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Vadim Pliner <Vadim.Pliner@VERIZONWIRELESS.COM>
Organization: http://groups.google.com
Subject:      Re: PROC LIFEREG
Comments: To: sas-l@uga.edu
In-Reply-To:  <OFC26CF4E1.7E3BB74F-ON88257022.0060CF0B-88257022.006180CF@epamail.epa.gov>
Content-Type: text/plain; charset="iso-8859-1"

>> 1) You recommended "...Add some extra variables and see if the
>> increase significantly improves your model."  Do you mean simply by
>> comparing the log-likelihood values?

DC> Yes.  The change in the log-likelihood will show the improvement
DC> (or lack thereof) in the model.

I would elaborate on that. When you add variables, i.e. parameters to
the log-likelihood, the maximized log-likelihood value will practically
always increase. I believe what matters is the magnitude of the
increase. Since you deal here with nested models, you can apply the
likelihood ratio test to tell if this magnitude is large enough. In
general, if k1 > k2 and LL(k1) & LL(k2) are the maximum log-likelihoods
of two models with all k1 parameters and k2 parameters not fixed by the
null hypothesis, respectively, then, under the null hypothesis,
2[LL(k1)-LL(k2)]  approximately follows a chi-square distribution with
(k1 - k2) degrees of freedom. For example, when adding a numeric
variable, k1 - k2 = 1 (you add 1 parameter). Low (not significant for a
chi-square distribution with 1 degree of freedom) values of
2[LL(k1)-LL(k2)] would suggest that adding this variable does not make
the model better statistically speaking.

HTH,
Vadim