Alternating Least Squares Optimal Scaling: Analysis of Nonmetric Data in Marketing Research

The authors discuss and illustrate the advantages and limitations of a family of new approaches to the analysis of metric and nonmetric data in marketing research. The general method, which is based on alternating least squares optimal scaling procedures, extends the analytical flexibility of the general linear model procedures (ANOVA, regression, canonical correlation, discriminant analysis, etc.) to situations in which the data (1) are measured at any mixture of the nominal, ordinal, or interval levels and (2) are derived from either a discrete or continuous distribution. The relationship of these procedures to traditional linear models and to other nonmetric approaches (such as multidimensional scaling and conjoint analysis) is reviewed.

[1]  S. S. Stevens Mathematics, measurement, and psychophysics. , 1951 .

[2]  J. Carroll,et al.  A New Measure of Predictor Variable Importance in Multiple Regression , 1978 .

[3]  Forrest W. Young,et al.  The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features , 1978 .

[4]  Vithala R. Rao,et al.  Conjoint Measurement- for Quantifying Judgmental Data , 1971 .

[5]  Forrest W. Young,et al.  Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features , 1976 .

[6]  William D. Perreault,et al.  Unequal Cell Sizes in Marketing Experiments: Use of the General Linear Hypothesis , 1975 .

[7]  Forrest W. Young,et al.  On the relation between undimensional judgments and multidimensional scaling , 1968 .

[8]  John A. Sonquist,et al.  Multivariate model building;: The validation of a search strategy , 1970 .

[9]  William D. Perreault,et al.  Alternative approaches for interpretation of multiple discriminant analysis in marketing research , 1979 .

[10]  Forrest W. Young,et al.  Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features , 1977 .

[11]  M. Kendall Statistical Methods for Research Workers , 1937, Nature.

[12]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[13]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[14]  G. Koch,et al.  Analysis of categorical data by linear models. , 1969, Biometrics.

[15]  J. Kruskal Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data , 1965 .

[16]  William D. Perreault,et al.  Classification for Market Segmentation: An Improved Linear Model for Solving Problems of Arbitrary Origin , 1977 .

[17]  Paul E. Green,et al.  On the Analysis of Qualitative Data in Marketing Research , 1977 .

[18]  C. Coombs A theory of data. , 1965, Psychology Review.

[19]  Forrest W. Young,et al.  Additive structure in qualitative data: An alternating least squares method with optimal scaling features , 1976 .

[20]  R. Shepard,et al.  A nonmetric variety of linear factor analysis , 1974 .

[21]  Forrest W. Young Methods for describing ordinal data with cardinal models , 1975 .

[22]  William D. Perreault,et al.  Validation of Discriminant Analysis in Marketing Research , 1977 .

[23]  Paul E. Green,et al.  Multidimensional Scaling: An Introduction and Comparison of Nonmetric Unfolding Techniques , 1969 .

[24]  R. M. Durand,et al.  Some Precautions in Using Canonical Analysis , 1975 .

[25]  William D. Perreault,et al.  QUANTIFYING MARKETING TRADE–OFFS IN PHYSICAL DISTRIBUTION POLICY DECISIONS , 1976 .

[26]  Louis Guttman,et al.  The Guttman-Lingoes nonmetric program series , 1973 .

[27]  Forrest W. Young Nonmetric multidimensional scaling: Recovery of metric information , 1970 .