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The Principal Components of Mixed Measurement Level Multivariate Data: An Alternating Least Squares Method with Optimal Scaling Features

Published online by Cambridge University Press:  01 January 2025

Forrest W. Young ,
Yoshio Takane  and
Jan de Leeuw
Forrest W. Young
Affiliation:
University of North Carolina
Yoshio Takane
Affiliation:
McGill University
Jan de Leeuw
Affiliation:
University of Leiden
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Abstract

A method is discussed which extends principal components analysis to the situation where the variables may be measured at a variety of scale levels (nominal, ordinal or interval), and where they may be either continuous or discrete. There are no restrictions on the mix of measurement characteristics and there may be any pattern of missing observations. The method scales the observations on each variable within the restrictions imposed by the variable's measurement characteristics, so that the deviation from the principal components model for a specified number of components is minimized in the least squares sense. An alternating least squares algorithm is discussed. An illustrative example is given.

Keywords

data analysisfactor analysisqualitative datanonmetric analysis
Type
Notes and Comments
Information
Psychometrika , Volume 43 , Issue 2 , June 1978 , pp. 279 - 281
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

Copies of this paper and of the associated PRINCIPALS program may be obtained by writing to Forrest W. Young, Psychometric Laboratory, Davie Hall 013-A, Chapel Hill, NC 27514.

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