Several questions are raised concerning differences
between traditional metric multiple regression,
which assumes all variables to be measured on interval
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 empirical
data composed of ordinally scaled variables. Results
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 addition,
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.
A common problem in data analysis involves
MacCallum, Robert C, Cornelius, Edwin T & Champney, Timothy. (1979). Validity and cross-validity of metric and nonmetric multiple regression. Applied Psychological Measurement, 3, 463-468. doi:10.1177/014662167900300404
MacCallum, Robert C.; Cornelius, Edwin T., III; Champney, Timothy.
Validity and cross-validity of metric and nonmetric multiple regression.
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