A hierarchical Bayesian finite mixture multidimensional scaling approach for accommodating structural and preference heterogeneity in three way preference data

Latent Class Multidimensional Scaling Models (LCMDS hereafter) have been widely used in the marketing and psychometric literature to capture consumers' preference heterogeneity and market structure simultaneously. In LCMDS analysis, two types of utility models, the vector and the ideal point model, have been used to represent consumers' preferences. These models, however, lead to different representations of market structure and consumers' heterogeneity. The ideal point model, a more general case of the vector model, often suffers from degenerate solutions. Recent research suggests that such ideal point degenerate solutions can be results of mixing sample of consumers that utilize different underlying utility functions. As such, we propose a Hierarchical Bayesian Finite Mixture MDS approach to take both preference and structural heterogeneity into account. We show that both the ideal point only model and the vector only model are special cases of the proposed model. We then discuss the Markov Chain Monte Carlo sampling utilized to generate the posterior distributions of the unknown model parameters. We then apply the model to simulated data, and an application from the pharmaceutical industry in the area of antidepressant prescriptions by medical doctors over time. We find that the model with structural and preference heterogeneity outperforms models without structural heterogeneity. Results suggest that ideal point segments and vector segments can be distinguished by their average prescription volume and preference variance. Vector segments exhibit higher prescription volume despite the fact that they consist of a small number of physicians than ideal point segments. Furthermore, vector segments show higher preference variance across brands. Together, this implies that the proposed approach can provide an efficient way of targeting physicians given that high volume physicians draw more attention for detailing effort but are less responsive to this marketing effort than low volume physicians.