This paper presents a new stochastic three-way unfolding
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 applying
this new method to synthetic datasets are presented.
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.
DeSarbo, Wayne S, Lehmann, Donald R, Holbrook, Morris B, Havlena, William J & et al. (1987). A stochastic three-way unfolding model for asymmetric binary data. Applied Psychological Measurement, 11, 397-418. doi:10.1177/014662168701100406
DeSarbo, Wayne S.; Lehmann, Donald R.; Holbrook, Morris B.; Havlena, William J.; Gupta, Sunil.
A stochastic three-way unfolding model for asymmetric binary data.
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