A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data

Applied Psychological Measurement, (1987) Vol. 11, No. 4, pp. 397-418

23 Pages Posted: 27 May 2016

See all articles by Wayne S. DeSarbo

Wayne S. DeSarbo

Pennsylvania State University

Donald R. Lehmann

Columbia Business School - Marketing

Morris Holbrook

Columbia University

William J. Havlena

Southern Methodist University (SMU)

Sunil Gupta

Harvard University - Business School (HBS)

Date Written: 1987

Abstract

This paper presents a new stochastic three-way un folding method designed to analyze asymmetric three- way, two-mode binary data. As in the metric three- way unfolding models presented by DeSarbo (1978) and by DeSarbo and Carroll (1980, 1981, 1985), this procedure estimates a joint space of row and column objects, as well as weights reflecting the third way of the array, such as individual differences. Unlike the traditional metric three-way unfolding model, this new methodology is based on stochastic assumptions using an underlying threshold model, generalizing the work of DeSarbo and Hoffman (1986) to three-way and asymmetric binary data. The literature concerning the spatial treatment of such binary data is reviewed. The nonlinear probit-like model is described, as well as the maximum likelihood algorithm used to estimate its parameter values. Results of a monte carlo study ap plying this new method to synthetic datasets are pre sented. The new method was also applied to real data from a study concerning word (emotion) associations in consumer behavior. Possibilities for future research and applications are discussed.

Suggested Citation

DeSarbo, Wayne S. and Lehmann, Donald R. and Holbrook, Morris and Havlena, William J. and Gupta, Sunil, A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data (1987). Applied Psychological Measurement, (1987) Vol. 11, No. 4, pp. 397-418, Available at SSRN: https://ssrn.com/abstract=2784492

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Donald R. Lehmann

Columbia Business School - Marketing ( email )

New York, NY 10027
United States

Morris Holbrook

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

William J. Havlena

Southern Methodist University (SMU) ( email )

6212 Bishop Blvd.
Dallas, TX 75275
United States

Sunil Gupta

Harvard University - Business School (HBS) ( email )

Soldiers Field Road
Morgan 270C
Boston, MA 02163
United States

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