Resemblance profiles as clustering decision criteria: Estimating statistical power, error, and correspondence for a hypothesis test for multivariate structure

Strategic categories and competition: significant clustering for strategic groups

Purpose

Strategic groups research has been hampered by the poor alignment between theory and methods. This has been due in large part to the lack of significance tests for cluster analysis. Now that significance tests are available, the theoretical and methodological implications are discussed. The paper aims to discuss these issues.

Design/methodology/approach

The theory behind strategic groups is reframed to capitalize on the available significance tests. Subsequently, the significance tests are also modified to fit the proposed theory. Due to this integrative approach, this is both a theoretical and a methodological paper.

Findings

In lieu of significance tests, finding differences in performance emerged as the litmus test for the existence of discrete strategic groups. The concept of strategic groups gradually evolved to fit this requirement. Now that significance tests are available, these legacy effects of the structure-performance link can be removed. This reveals that three conflicting concepts have been sharing the label of strategic groups: strategic categories, interdependent strategic groups and strategic performance groups. The theory also reveals that the significance tests developed in ecological research need modifications for use in strategic groups research.

Research limitations/implications

A theory is proposed for interdependent strategic groups and a significance test of external isolation is proposed as part of this integrative solution.

Originality/value

This integrative solution appears to resolve the historical mismatch between theory and methods that has plagued this field since its inception. This creates a variety of intriguing areas for future research.

Resemblance profiles as clustering decision criteria: Estimating statistical power, error, and correspondence for a hypothesis test for multivariate structure

Clustering data continues to be a highly active area of data analysis, and resemblance profiles are being incorporated into ecological methodologies as a hypothesis testing‐based approach to clustering multivariate data. However, these new clustering techniques have not been rigorously tested to determine the performance variability based on the algorithm's assumptions or any underlying data structures. Here, we use simulation studies to estimate the statistical error rates for the hypothesis test for multivariate structure based on dissimilarity profiles (DISPROF). We concurrently tested a widely used algorithm that employs the unweighted pair group method with arithmetic mean (UPGMA) to estimate the proficiency of clustering with DISPROF as a decision criterion. We simulated unstructured multivariate data from different probability distributions with increasing numbers of objects and descriptors, and grouped data with increasing overlap, overdispersion for ecological data, and correlation among descriptors within groups. Using simulated data, we measured the resolution and correspondence of clustering solutions achieved by DISPROF with UPGMA against the reference grouping partitions used to simulate the structured test datasets. Our results highlight the dynamic interactions between dataset dimensionality, group overlap, and the properties of the descriptors within a group (i.e., overdispersion or correlation structure) that are relevant to resemblance profiles as a clustering criterion for multivariate data. These methods are particularly useful for multivariate ecological datasets that benefit from distance‐based statistical analyses. We propose guidelines for using DISPROF as a clustering decision tool that will help future users avoid potential pitfalls during the application of methods and the interpretation of results.