A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data

Wayne S. Desarbo, Donald R. Lehmann, Morris B. Holbrook, William J. Havlena, Sunil Gupta

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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.

Original languageEnglish (US)
Pages (from-to)397-418
Number of pages22
JournalApplied Psychological Measurement
Volume11
Issue number4
DOIs
Publication statusPublished - Dec 1987

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All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)

Cite this

Desarbo, W. S., Lehmann, D. R., Holbrook, M. B., Havlena, W. J., & Gupta, S. (1987). A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data. Applied Psychological Measurement, 11(4), 397-418. https://doi.org/10.1177/014662168701100406