, Volume 41, Issue 4, pp 505-529

First online:

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

  • Forrest W. YoungAffiliated withPsychometric Laboratory, University of North Carolina
  • , Jan de LeeuwAffiliated withRijksuniversiteit Te Leiden
  • , Yoshio TakaneAffiliated withPsychometric Laboratory, University of North Carolina

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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.

Key words

linear model canonical analysis measurement multivariate data survey data successive block algorithm