Technical Note—Testing Competitive Market Structures: An Application of Weighted Least Squares Methodology to Brand Switching Data

Weighted least squares (WLS) analysis of categorical data is used to provide a general framework for the analysis of brand switching data. As in an earlier approach described by Urban, Johnson, and Hauser (Urban, G. L., P. L. Johnson, J. R. Hauser. 1984. Testing competitive market structures. (2, Spring) 83–112.), a forced switching matrix of first and second choice brands is created, and a partitioning scheme that places brands into mutually exclusive partitions is identified. Then, using the WLS approach, the off-diagonal elements of the forced switching matrix are transformed into dependent variables in a linear model. The dependent variables specify whether observed switching of brands within the hypothesized partitions is greater or less than would be expected based upon the market shares of the brands. Chi-square statistics, in the context of a linear model, are used to test the goodness of the partitioning scheme as a whole and for individual brands, and to evaluate partition homogeneity by testing whether the level of switching within a partition is the same for each brand. Parsimonious models which explain brand-to-partition switching can be identified.