A Hybrid External Multidimensional Unfolding Approach for the Analysis of Self-Similarity Emotion Judgments
Sparks, Jordan Lea
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A hybrid model approach to Carroll’s hierarchy of preference models (1972) is presented to 1) provide a more parsimonious fit for preference judgments, 2) minimize the number of anti-ideal points that typically arise from External Multidimensional Unfolding (EMDU) models, and 3) guarantee that all model terms are statistically significant. The term “hybrid model” refers to situations in which the optimal regression model within Carroll’s hierarchy has terms that are not all statistically significant, and consequently, such terms are eliminated. This elimination of terms from Carroll’s original models leads to hybrid models in which alternative representations of preference may operate across stimulus dimensions. This is in stark contrast to Carroll’s original models which assume that preference operates identically across all dimensions. This methodology was grounded in the idea that there may be a few interpretable anti-ideal points in an EMDU solution, but they should account for a statistically significant amount of variation in the preference responses. The new approach was applied to self-similarity judgments in the context of facial affect. Specifically, photos depicting facial emotions were scaled using multidimensional scaling of pairwise similarity judgments among photos, and then 1,564 subjects were located jointly in that same emotion space using single-photo, self-similarity judgments. When the optimal model was selected for each subject, more than 95% of these models were hybrids rather than traditional models. Additionally, this new approach reduced the number of anti-ideal points by approximately 25% by allowing these points to become vectors in the group space. The results of this research illustrate that a hybrid approach to EMDU is an intuitive extension of Carroll’s hierarchy that can provide more parsimonious fit, reduce the number of anti-deal points, and represent preferences across stimulus dimensions in a less “all-or-none” fashion.