Seminar Notice

Statistical Laboratory

Iowa State University

DATE AND TIME:  Monday, November 1, 2004 4:10PM

PLACE:  319 Snedecor

SPEAKER: Joseph E. Cavanaugh, Department of Biostatistics, The University of Iowa, Iowa City

TITLE:  Criteria for Linear Model Selection

ABSTRACT

Model selection criteria frequently arise from constructing estimators of discrepancy measures used to assess the disparity between the "true" model and a fitted approximating model.  The Akaike (1973) information criterion and its variants result from utilizing Kullback's (1968) directed divergence as the targeted discrepancy.  The directed divergence is an asymmetric measure of separation between two statistical models, meaning that an alternate directed divergence may be obtained by reversing the roles of the two models in the definition of the measure.  The sum of the two directed divergences is Kullback's (1968) symmetric divergence.

In the framework of linear models, a comparison of the two directed divergences indicates an important distinction between the measures.  When used to evaluate fitted approximating models which are improperly specified, the directed divergence which serves as the basis for AIC is more sensitive towards detecting overfit models, whereas its counterpart is more sensitive towards detecting underfit models.  Since the symmetric divergence combines the information in both measures, it functions as a gauge of model disparity which is arguably more balanced than either of its individual components.  With this motivation, we propose a new class of criteria for linear model selection based on targeting the symmetric divergence.  Our criteria may be regarded as analogues of AIC and two of its variants: "corrected" AIC or AICc (Sugiura, 1978; Hurvich and Tsai, 1989), and "modified" AIC or MAIC (Fujikoshi and Satoh, 1997).  We examine the selection tendencies of the new criteria in a simulation study.  Our results indicate that the new criteria perform favorably against their AIC analogues.

We close with a brief review of current work on the development and investigation of model selection criteria based on the symmetric divergence.  Some of this work introduces new criteria by devising alternate ways of estimating the discrepancy.  Other work extends the justification and applicability of criteria from the fundamental setting of linear models to other modeling frameworks (e.g., nonlinear regression, logistic regression, autoregression).

COFFEE:  3:45 p.m., 104 Snedecor