A new clustering methodology for the analysis of sorted or categorized stimuli

Abstract

This paper introduces a new stochastic clustering methodology devised for the analysis of categorized or sorted data. The methodology reveals consumers' common category knowledge as well as individual differences in using this knowledge for classifying brands in a designated product class. A small study involving the categorization of 28 brands of U.S. automobiles is presented where the results of the proposed methodology are compared with those obtained from KMEANS clustering. Finally, directions for future research are discussed.A wide range of methods and procedures exists for the analysis of similarity relations among stimuli. These methods range from traditional spatial multidimensional scaling methods (Shepard 1962;Kruskal 1964) to network clustering methods (Johnson 1967;Shepard and Arabie 1979). The input to such procedures is typically some measure of similarity, whether obtained from paired comparison judgments, or derived from some similarity-based response (e.g., sorting data, classification errors, preference relations, or choice data). One such class of input proximity data is the sorting of stimuli (on the basis of their similarity) into homogeneous subsets or categories. Sorting tasks are employed in a wide range of basic and applied research contexts. When subjects face a. large number of stimuli (Rao and Katz 1971) or have a limited ability to respond (Horton and Markm~ 1980), a sorting task may be gainfully employed.Unfortunately, traditional methods may be ill-suited to this particular type of similarity-based response. Such methods may not capture the category perceptions that underlie the sorting task or the individual differences involved. Our goal is to describe a new clustering methodology designed specifically for the analysis

Understanding consumer usage of product magnitudes through sorting tasks

“…However, a sorting task has several characteristics that make it a very suitable alternative for examining how consumers think about product attributes, and specifically magnitude estimation. Foremost, a sorting task is a natural way of revealing a respondent's internal perceptions or knowledge base (DeSarbo, Jedidi, & Johnson, 1991). A sorting task is open-ended, and, unlike category scaling, does not impose a certain number of categories on the respondents.…”

Revisiting attribute diagnosticity in the context of product typicality

“…Little research has been done on the categorization of products associated with several different categories (cf. DeSarbo, Jedidi, & Johnson, 1991). It seems necessary to investigate a determinant of typicality that can be useful for understanding the categorization of ambiguous products.…”

Extracting Summary Piles from Sorting Task Data

“…More recently, researchers have also modeled the sorting data directly by making assumptions about the underlying latent categorization process regarding the items being sorted into the same piles (i.e., the piles are the realized behavior of the underlying category structures). DeSarbo, Jedidi, and Johnson (1991) and Blanchard et al (2012) propose latent structure models that identify the unobserved categories that consumers perceive in a set of items, with the assumption that y ijk follows a Bernoulli distribution based on pairwise latent similarity judgments. Note that their procedures cannot accommodate the wide variety of sorting tasks that are not based on a latent pairwise similarity process (e.g., choice context, preferences).…”

“…Their model assumes that these pairwise counts are generated from a pairwise Poisson process with a gamma-distributed rate that is also a function of a latent pairwise similarity judgment between pairs of items. As is true in the research of DeSarbo, Jedidi, and Johnson (1991) and Blanchard et al (2012), the procedures involve conditional maximum likelihood estimates (MLEs) of the parameters through numerical optimization; here, the model's optimization (MLE) computation requirements are quite extensive, even for moderately sized marketing research applications (e.g., 100–150 participants, 20–50 items). Most importantly, these parametric models proposed are not appropriate unless one knows that the piles are formed by a cognitive process relying on pairwise similarity judgments.…”