Assessing the Dissimilarity Profiles Test for Significant Clustering: Is It Suitable for Strategic Groups Research?

Research on strategic groups has been hindered by the lack of significance testing in cluster analysis. Consequently, researchers cannot determine if a cluster analysis has invented statistical groupings as an analytic convenience or actually discovered discrete strategic groups that could constitute pockets of oligopolistic competition within that industry. Ideally, a permutation technique would impose the conditions of the null hypothesis (no clustering) while preserving all of the other characteristics of that data. Unfortunately, the closest approximation for cluster analysis is achieved by independently permuting each variable. This destroys all multivariate structure in the data including, but not limited to, multivariate clustering. Hence, a significant result indicates the existence of multivariate structure which might include multivariate clustering. Further, this permutation approach cannot detect univariate clustering. Several programs have recently become available. A Monte Carlo study examines the dissimilarity profiles function in the Fathom toolbox in Matlab. Type I and Type II error rates as well as clustering accuracy are reported for a variety of conditions that are relevant for strategic groups’ research. Under favorable conditions, this program is remarkably powerful, but under less favorable conditions, the results are horribly misleading. A permutation test should not be used alone. A multimethod approach is proposed that exploits the complementarity of a permutation test and a Monte Carlo test; the weaknesses of one correspond to the strengths of the other. Indeed, the Monte Carlo test specifically rules out the most troubling source of Type I errors for the permutation test.