Capturing Individual Differences in Paired Comparisons: An Extended BTL Model Incorporating Descriptor Variables

Abstract

The method of paired comparisons addresses the problem of determining the scale values of a set of stimuli on a preference continuum that is not directly observable. The conventional approach in analyzing paired comparisons is to view all individuals as homogeneous and estimate a single vector of scale values for the stimuli. The authors describe an extended BTL model, a simultaneous segmentation and estimation procedure for paired comparisons that can also accommodate descriptor variables, if available. The procedure extends methods for analyzing paired comparisons in two important ways. First, recognizing that individuals may be heterogeneous in their preference structure, the model attempts to group individuals into segments, where individuals belonging to the same segment can be characterized adequately by a segment-specific set of scale values. Second, the model allows descriptor variables to be incorporated into the analysis. Though incorporating descriptor variables in the analysis of paired comparisons entails some additional estimation issues, the ability to calibrate stimulus scale values for different market segments and to understand the potential reasons why the relative locations of the stimuli as perceived by persons making the judgments vary according to the latent segment to which an individual belongs appears to be an extremely useful feature of the proposed method.