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Applied Psychological Measurement, Vol. 11, No. 4, 397-418 (1987)
DOI: 10.1177/014662168701100406

A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data

Wayne S. DeSarbo

University of Pennsylvania

Donald R. Lehmann

Columbia University

Morris B. Holbrook

Columbia University

William J. Havlena

Southern Methodist University

Sunil Gupta

University of California, Los Angeles

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.


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