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Quantitative Analysis of Qualitative Data

Published online by Cambridge University Press:  01 January 2025

Forrest W. Young
Forrest W. Young*
Affiliation:
L. L. Thurstone Psychometric Laboratory University of North Carolina At Chapel Hill
*
Requests for reprints should be sent to Forrest Young, Psychometric Lab, UNC, Davie Hall, 013-A, Chapel Hill, N.C. 27514.
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Abstract

This paper presents an overview of an approach to the quantitative analysis of qualitative data with theoretical and methodological explanations of the two cornerstones of the approach, Alternating Least Squares and Optimal Scaling. Using these two principles, my colleagues and I have extended a variety of analysis procedures originally proposed for quantitative (interval or ratio) data to qualitative (nominal or ordinal) data, including additivity analysis and analysis of variance; multiple and canonical regression; principal components; common factor and three mode factor analysis; and multidimensional scaling. The approach has two advantages: (a) If a least squares procedure is known for analyzing quantitative data, it can be extended to qualitative data; and (b) the resulting algorithm will be convergent. Three completely worked through examples of the additivity analysis procedure and the steps involved in the regression procedures are presented.

Keywords

exploratory data analysisdescriptive data analysismultivariate data analysisnonmetric data analysisalternating least squaresscalingdata theory
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 357 - 388
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

Presented as the Presidential Address to the Psychometric Society's Annual meeting, May, 1981. I wish to express my deep appreciation to Jan de Leeuw and Yoshio Takane. Our “team effort” was essential for the developments reported in this paper. Without this effort the present paper would not exist. Portions of this paper appear in Lantermann, E. D. & Feger, H. (Eds.) Similarity and Choice, Hans Huber, Vienna, 1980. The present paper benefits greatly from a set of detailed comments made by Joseph Kruskal on the earlier paper.

References

Reference Notes

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