The HPREDUCE Procedure

Criteria Used in Model Selection

The HPREDUCE procedure supports the following three fit statistics that you can specify as stopping criteria in the REDUCE statement:

AIC: Akaike’s information criterion (Akaike 1969; Judge et al. 1985)
AICC: Corrected Akaike’s information criterion (Hurvich and Tsai 1989)
BIC: Schwarz Bayesian information criterion (Schwarz 1978; Judge et al. 1985)

The HPREDUCE procedure supports multiple response variables; therefore, it computes the AIC, AICC, and BIC that are defined for multivariate regression. Besides the three criteria, it also computes the error sum of squares (SSE) and residual mean square error (MSE).

Table 9.3 provides formulas and definitions for these fit statistics.

Table 9.3: Formulas and Definitions for Model Fit Summary Statistics

Statistic	Definition or Formula
n	Number of observations
p	Number of parameters
t	Number of response variables in supervised selection; number of unselected variables in unsupervised selection
	Error sum of squares