## THE SCHWARZ CRITERION AND RELATED METHODS FOR MODEL SELECTION IN LINEAR REGRESSION

September, 1995

Tech Report

Donna K. Pauler

### Abstract

The Schwarz criterion or Bayesian information criterion provides a simple reference method for choosing between competing Normal linear regression models. Indeed, it can be computed directly from output of standard regression software. In this paper we motivate the Schwarz criterion and two modifications of it by showing them to correspond asymptotically to Bayes factors which use intuitively appealing "unit-information" priors (Kass and Wasserman (1995)). The first modification of the Schwarz criterion allows for inclusion of a general, possibly informative prior. The second corresponds asymptotically to the the Bayes factors of Zellner and Siow (1980), O'Hagan (1995), and is similar to the Bayes factor of Berger and Pericchi (1994). By way of two examples, we show that the Schwarz criterion and its modifications can be quite accurate approximations for even small sample sizes.