RE: Minimum value of objective function..

From: "Bachman, William" <bachmanw@globomax.com> Subject: RE: Minimum value of objective function.. Date: Fri, 5 Oct 2001 12:09:37 -0400 In answer to your question, the numerical value of the objective function has no meaning by itself. The value will depend, among other things, on the amount of data you have. The number can be large, small or even negative. By itself, it says nothing about your model. It is related to the sum of squared errors (more complicated than this in actuality). It is important only in a relative sense. Relative to the objective function value of a competing model. One typically compares two model objective functions using some selected criterion. For non-nested models, one could use the Aikaike Information Criterion (AIC) (the objective function plus two times the number of parameter) to compare the models. The lower AIC is "better". For nested models, you can use the likelihood ratio test. With the likelihood ratio test, you assume the difference in objective functions between the two models is chi squared distributed. You then make a decision as to which model is "better" based on a preselected significance level, the degrees of freedom (difference in total number of parameters in the models) and the critical chi square value (for the chosen level of significance and degrees of freedom). If a nested model with fewer parameters has an objective function value lower by an amount larger than the critical chi square value than the "larger" model, than it is the "better" model. Do not use the difference in objective function value as the sole criterion of goodness-of-fit. It is possible to have a lower objective function value and a worse fit. Also consider, the change in magnitude of the variance parameters and the diagnostic plots. William J. Bachman, Ph.D. GloboMax LLC 7250 Parkway Dr., Suite 430 Hanover, MD 21076 Voice (410) 782-2212 FAX (410) 712-0737 bachmanw@globomax.com