A Three-Way Clusterwise Bilinear Multidimensional Scaling Methodology for the Spatial Representation of Dynamic Preferences

S. ATALAY, S. Blanchard, W. DeSarbo

Computational Statistics and Data Analysis

June 15 2009, vol. 53, n°8, pp.3217-3230

Departments: Marketing

Keywords: Simultaneous classification, Degenerate solutions, Linear-regression, Vector model, Behavior, Variables, Perspective, Decisions, Component, Ratings

Various deterministic and latent structure approaches for combining forms of multidimensional scaling and cluster analysis have been previously discussed. A new clusterwise three-way unfolding methodology for the analysis of two-way or three-way metric dominance/preference data is proposed. The purpose of this proposed methodology is to simultaneously estimate a joint space of stimuli and cluster ideal point representations, as well as the clusters themselves, such that the geometry underlying the clusterwise model renders some indication of the underlying structure in the data. In the three-way case, it is shown how multiple ideal points can represent preference change over contexts or situations. Partitions, overlapping clusters, stationary and context dependent preference representations are allowed. After a literature review of related methodological research, the technical details of the proposed three-way clusterwise spatial unfolding model are presented in terms of modeling context/situational dependent preferences (i.e., preferences for various stimuli collected over the same set of subjects over time, situation, etc.). The psychological basis for the models is provided in terms of the extensive behavioral decision theory and consumer psychology literature on contextual preferences and situational effects. An application to a data set exploring preferences for breakfast/snack food data over a number of different usage situations is then presented, followed by a discussion on future potential research directions.