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

Charles Carroll, Kelly van Heyningen

Abstract


a. Introduction: 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.

b. Literature review/research gap: 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.

c. Research method: Several programs have recently become available. A Monte Carlo study examines the DISPROF 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.

d. Findings: Under favourable conditions, this program is remarkably powerful, but under less favourable conditions, the results are horribly misleading.

e. Theoretical and practitioner implications: 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.


Keywords


cluster analysis; permutation test; significance testing; strategic groups; Monte Carlo study

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References


Barney, J. B., & Hoskisson, R. E. (1990). Strategic groups: Untested assertions and research proposals. Managerial and Decision Economics, 11, 187-198.

Brewer, J., & Hunter, A. (2006). Foundations of Multimethod Research: Synthesizing Styles. Thousand Oaks, CA: SAGE Publications.

Brandenburger, A. M., & Nalebuff, B. J. (1996). Co-opetition. New York: Currency Doubleday.

Carroll, C. (2006). Canonical correlation analysis: Assessing links between multiplex networks. Social Networks, 28, 310–330.

Clarke, K. R., & Gorley, R. N. (2015). PRIMER v7: User Manual/Tutorial [Computer software and manual]. Plymouth, UK: PRIMER-E. Retrieved August 15, 2015, from http://www.primer-e.com/downloads.htm

Clarke, K. R., Somerfield, P. J., & Gorley, R. N. (2008). Testing null hypotheses in exploratory community analyses: Similarity profiles and biota-environmental linkage. Journal of Experimental Marine Biology and Ecology, 366, 56-69.

Harrigan, K. R. (1985). An application of clustering for strategic group analysis. Strategic Management Journal, 6, 55-73.

Hatten, K. J., & Hatten, M. L. (1987). Strategic groups, asymmetrical mobility barriers and contestability. Strategic Management Journal, 8(4), 329-342.

IBM Corporation (2016). IBM SPSS Statistics 24 Command Syntax Reference [Manual]. Retrieved January 17, 2017 from ftp://public.dhe.ibm.com/software/analytics/spss/documentation/statistics/24.0/en/server/Manuals/IBM_SPSS_Statistics_Command_Syntax_Reference.pdf

Jones, D. L. (2015). Fathom Toolbox for Matlab: software for multivariate ecological and oceanographic data analysis [Computer software]. St. Petersburg, FL: College of Marine Science, University of South Florida. Retrieved August 15, 2015, from http://www.marine.usf.edu/user/djones/

Ketchen, D. J., & Shook, C. L. (1996). The application of cluster analysis in strategic management research: An analysis and critique. Strategic Management Journal, 17(6), 441-458.

Kline, R. B. (2004). Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, D.C.: APA Books.

Legendre, P., & Legendre, L. (1998). Numerical ecology (2nd English ed.). Amsterdam: Elsevier Science.

Mair, P., Satorra, A., & Bentler, P. M. (2012). Generating nonnormal multivariate data using copulas: Applications to SEM. Multivariate Behavioral Research, 47(4), 547–565. https://doi.org/10.1080/00273171.2012.692629

McGee, J., & Thomas, H. (1986). Strategic groups: Theory, research and taxonomy. Strategic Management Journal, 7, 141-160.

McKelvey, B. (1982). Organizational systematics: Taxonomy, evolution, classification. Berkeley: University of California Press.

Milligan, G. W. (1981). A Monte Carlo study of thirty internal criterion measures for cluster analysis. Psychometrika, 46(2), 187-199.

Nath, D., & Gruca, T. S. (1997). Convergence across alternative methods for forming strategic groups. Strategic Management Journal, 18(9), 745-760.

Porter, M.E. (1979). The structure within industries and companies’ performance. Review of Economics and Statistics, 61(2), 214–227.

Scheibler, D., & Schneider, W. (1985). Monte Carlo tests of the accuracy of cluster analysis algorithms: A comparison of hierarchical and nonhierarchical methods. Multivariate Behavioural Research, 20, 283-304.

Somerfield, P. J., & Clarke, K. R. (2013). Inverse analysis in non-parametric multivariate analyses: Distinguishing groups of associated species which covary coherently across samples. Journal of Experimental Marine Biology and Ecology, 449, 261–273.

Tang, M.-J., & Thomas, H. (1992). The concept of strategic groups: Theoretical construct or analytical convenience. Managerial and Decision Economics, 13(4), 323-329.

Ward, J. H., Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236-244.

Whitaker, D., & Christman, M. (2014). Clustsig: Significant cluster analysis [Computer software and manual]. Retrieved August 15, 2015, from https://cran.r-project.org/web/packages/clustsig/index.html

Xu, L., Bedrick, E. J., Hanson, T., & Restrepo, C. (2014). A comparison of statistical tools for identifying modality in body mass distributions. Journal of Data Science, 12, 175-196.


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