A Parametric Multidimensional Unfolding Procedure for Incomplete Nonmetric Preference/Choice Set Data in Marketing Research

Abstract

Multidimensional unfolding (MDU) is one of the most powerful conceptual and methodological tools used in marketing for product positioning analysis. Unfortunately, the majority of the commercial software programs available for performing such analyses (especially nonmetric analyses) suffer from serious limitations including degenerate solutions, interpretation difficulties, lack of supporting statistical inference and model selection procedures, excessive number of parameters to estimate, requirements of full data sets, and difficulties with local optima. The authors propose a new parametric approach to nonmetric unfolding (PARFOLD) to extend methodological developments in the econometrics and marketing science arenas. The authors develop the technical aspects of the proposed procedure, including options for accommodating incomplete rank orders, constraints, and reparameterizations. Two marketing-related applications are provided: one deals with preferences for snack food items involving complete rank orders, and the second involves incomplete data in which students rank order Master of Business Administration schools in their consideration/application sets. Comparisons are made with existing nonmetric MDU procedures including ALSCAL, PREFMAP, and KYST with respect to several newly proposed diagnostic indices of solution degeneracy and positioning implications. Finally, the authors summarize limitations of the proposed model and offer directions for further research.