A Stochastic Three-Way Unfolding Model for Asymmetric Binary Data

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.