A CONTINGENCY ANALYSIS APPROACH TO PERCEPTUAL MAPPING

GLEN RALPH JARBOE, Purdue University

Abstract

This study develops and illustrates a method for the analysis of simple associative data (dichotomous judgments) in terms of geometric object/attribute configurations. Data of this type has traditionally been analyzed by aggregating it across individual subjects into the form of contingency tables. It is shown that if certain assumptions may be made about the process of generating associative data, it may be possible to find appropriate transformations such the aggregate response patterns of homogeneous groups may be faithfully represented in the form of geometric configurations. Transformation models are developed to relate manifest data to theoretical models of the data generating process. These models are then tested in a monte carlo simulation which generates simple associative data which differ with respect to the number of subjects, products, product attributes, level and type of error, and underlying dimensionality. The data utilized include three-category, two-category, and first-choice data. A computer algorithm performs the desired transformations, computes a derived similarities matrix and performs Eckhart-Young decomposition. The results indicate that, even in data sets as small as 50 subjects, these models are capable of recovering the underlying structure of the data with a high degree of accuracy. Finally, two of the models are applied to the measurement and analysis of retail image utilizing data from an earlier study of the retail grocery market in a major metropolitan area. Perceptual maps are constructed which not only have a high degree of face validity but also yield conclusions that are consistent with those derived by more traditional methods of analysis. However, the present results are especially appealing in that they are more parsimoniously presented and the ramifications of various managerial actions may be more clearly assessed. The value of perceptual mapping and market structure analysis as a style of data analysis and presentation has long been recognized. However, its very stringent data requirements have diminished its utility to all but the largest firms with substantial research budgets. The present work demonstrates that by relying upon simpler data gathering methods and appropriate analysis techniques, this type of analysis may be performed at substantially lower cost with only a small loss in the precision of the results.

Degree

Ph.D.

Subject Area

Marketing

COinS