Interpreting Degenerate Solutions in Unfolding by Use of the Vector Model and the Compensatory Distance Model

Abstract

unfolding, degeneracy, mixed plots, squared correlation, iterative majorization,

A cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals

“…The representation step minimizes the weighted average of the squared residuals between Sokal-Michener dissimilarities and a ratio transformation of the between-cluster distances. This procedure is equivalent to maximizing squared correlations, similar to the method proposed by Van Deun et al (2005). After the estimation, an identification step is performed for the distances so that the overall stress can be evaluated.…”

“…A computationally efficient procedure in unfolding for large data sets (without clustering) was proposed by Van Deun et al. (2005, 2007). The optimization procedure used, in terms of squared correlations, is equivalent to minimizing Kruskal's Stress‐2 measure (Van Deun et al., 2005).…”

“…(2005, 2007). The optimization procedure used, in terms of squared correlations, is equivalent to minimizing Kruskal's Stress‐2 measure (Van Deun et al., 2005).…”

“…However, in some experimental situations, clustering is natural for individuals but not for objects, and when a large number of objects must be handled, the computational cost rises considerably. A computationally efficient procedure in unfolding for large data sets (without clustering) was proposed by Van Deun et al (2005. The optimization procedure used, in terms of squared correlations, is equivalent to minimizing Kruskal's Stress-2 measure (Van Deun et al, 2005).…”

A Hierarchical Bayesian Multidimensional Scaling Methodology for Accommodating Both Structural and Preference Heterogeneity

“…Recent research, however, suggests that this may not be the case. Deun, Groenen, Heiser, Busing, and Delbeke (2005) contended, in the context of traditional MDS, that there is a close connection between the vector model and degenerate solutions frequently encountered in the ideal point model, and that those ideal points farther from the centroid of stimuli coordinates can be replaced by vectors without altering subjects' preference order. This implies that combinations of the vector model and the ideal point model need to be explicitly considered, and that a generalized approach which can explicitly identify "mixtures of vector and unfolding (ideal point) representations" (DeSarbo & Carroll, 1985) would be an important contribution to the MDS literature.…”