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Extra resources for Boards, Incentives, and CSR
If one were to move an ideal point for any individual consumer further and further out along a ﬁxed line from the origin while holding the brand locations ﬁxed, one ends up with a vector utility model for that consumer in the limit where the ideal point tails off to inﬁnity. The family of concentric circles surrounding that ideal point begins to ﬂatten out and resemble the iso-preference lines of the vector model. Thus, there is additional ﬂexibility involved in the simple unfolding model which can accommodate the vector model as a special case.
2. The segment level or clusterwise multidimensional unfolding model DeSarbo et al. (2008) more recently developed a two- and three-way clusterwise unfolding MDS model which simultaneously estimates a joint space of stimuli and (multiple) ideal points by derived segment, as well as the segments themselves. This model is mathematically represented as: F(Pijr )−1 = S T θis s=1 wrt (asrt − bjt )2 + cr + eijr , (8) t=1 where r = 1, . . ); Pijr = the preference for brand j given by consumer i in situation r· ; asrt = the tth coordinate of the ideal point for market segment s in situation r· ; wrt = weighting parameters for dimension t in situation r· ; cr = an additive constant for situation r· ; eijr = error (deterministic).
Different from the simple unfolding model, this model has ellipse shaped iso-preference contours (instead of concentric circles in the simple unfolding model) in two dimensions where the larger the weight for a particular dimension, the smaller the corresponding axis of the iso-preference ellipse. In Fig. 3, Consumer 1 equally weights the two dimensions and orders brands A, B, C, D regarding his predicted preference; Consumer 2 weights Dimension I more than Dimension II with the preference order of C, D, A, B; and Consumer 3 weights Dimension II more than Dimension I with the preference order of B, D, A, C.