Validity and Cross-Validity of Metric and Nonmetric Multiple Regression

Abstract

Several questions are raised concerning differences between traditional metric mutiple regression, which assumes all variables to be measured on in terval scales, and nonmetric multiple regression, which treats variables measured on any scale. Both models are applied to 30 derivation and cross- validation samples drawn from two sets of empiri cal data composed of ordinally scaled variables. Re sults indicate that the nonmetric model is, on the average, far superior in fitting derivation samples but that it exhibits much more shrinkage than the metric model. The metric technique fits better than the nonmetric in cross-validation samples. In ad dition, results produced by the nonmetric model are more unstable across repeated samples. A probable cause of these results is presented, and the need for further research is discussed.