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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, PREFMAR 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.

A multidimensional scaling methodology (STUNMIX) for the analysis of subjects' preference/choice of stimuli that sets out to integrate the previous work in this area into a single framework, as well as to provide a variety of new options and models, is presented. Locations of the stimuli and the ideal points of derived segments of subjects on latent dimensions are estimated simultaneously. The methodology is formulated in the framework of the exponential family of distributions, whereby a wide range of different data types can be analyzed. Possible reparameterizations of stimulus coordinates by stimulus characteristics, as well as of probabilities of segment membership by subject background variables, are permitted. The models are estimated in a maximum likelihood framework. The performance of the models is demonstrated on synthetic data, and robustness is investigated. An empirical application is provided, concerning intentions to buy portable telephones.

The authors propose a new methodology for deriving hierarchical product-market structures from disaggregate purchase data. A hierarchical product-market tree is estimated from scanner panel purchase data in a maximum likelihood framework. The derived product-market representation portrays both products and market segments as terminal nodes in a hierarchical tree where the “closer” a product is to a particular segment, the higher its revealed preference for that product. The hierarchical representation of products and segments as well as the composition of the market segments are derived simultaneously. An empirical application examines the descriptive and predictive validity of the methodology.

The authors present a new multidimensional unfolding methodology that can analyze various types of individual choice data. The model represents choice data, defined by dichotomous variables that indicate whether a particular brand was chosen or not, in terms of a joint space of consumers and brands. Explicit treatment of marketing and subject background variables is allowed through optional model reparameterizations of consumers and brands. Together with the joint space representation of both consumers and brands, these optional reparameterizations can provide information on appropriate market segmentation bases and respective product positioning strategies. The authors apply this spatial choice model to data on consumer (intended) choices for 12 residential communications devices and demonstrate how the results can be used for optimal positioning decisions.