, Volume 41, Issue 4, pp 505-529

Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features

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Abstract

A method is discussed which extends canonical regression analysis to the situation where the variables may be measured at a variety of levels (nominal, ordinal, or interval), and where they may be either continuous or discrete. There is no restriction on the mix of measurement characteristics (i.e., some variables may be discrete-ordinal, others continuous-nominal, and yet others discrete-interval). The method, which is purely descriptive, scales the observations on each variable, within the restriction imposed by the variable's measurement characteristics, so that the canonical correlation is maximal. The alternating least squares algorithm is discussed. Several examples are presented. It is concluded that the method is very robust. Inferential aspects of the method are not discussed.

This research was partially supported by grants MH10006 and MH26504 from the National Institute of Mental Health to the Psychometric Laboratory of the University of North Carolina. Portions of the research reported here were presented to the spring meeting of the Psychometric Society, 1975. We wish to thank John B. Carroll and Elliot M. Cramer for their critical evaluations of an earlier draft of this report, and Jack Hoadley and John B. Carroll for letting us use their data. Copies of the paper may be obtained from the first author.
Yoshio Takane can be reached at the Department of Psychology, University of Tokyo, Tokyo, Japan.