Clustering Firms into Strategic Groups

Strategic management research generally focuses on the relationships among strategy, environment, organization, and performance. The multi-dimensionality of these constructs creates a conceptual challenge in that a vast array of combinations could be developed along these dimensions to describe firms (Ketchen et al. 1996). The conceptual idea of cluster analysis is to take a sample of elements and group them so that the statistical variance among elements grouped together is minimized while between-group variance is maximized. Cluster

36 E.g., log transformation squashes the right tail of the distribution, square root transformation brings large scores closer to the center, and reciprocal transformation reduces the impact of large scores and increases the impact of small scores.

37 Pearson’s product-movement correlation coefficient is an example of a bivariate correlation coefficient. A one-tailed test should be selected for a directional hypothesis, whereas a two-tailed test should be used when the nature and direction of the relationship is unknown. Considerable caution must be taken when interpreting correlation coefficients because they give no indication of the causality’s direction. Correlation coefficients say nothing about which variable causes the other to change. Moreover, in any bivariate correlation causality between two variables cannot be assumed because there may be other measured or unmeasured variables affecting the results (this is known as the ‘third variable problem’ or the

‘tertium quid’). Spearman’s correlation coefficient is an alternative test and a non-parametric statistic. It can be used when the data has violated parametric assumptions.

analysis is a statistical technique that sorts observations into similar sets or groups. Distances between groups approximate the height of mobility barriers.

The use of cluster analysis presents a complex challenge because it requires several methodological choices that determine the quality of a cluster solution, and the implementation of cluster analysis in strategic management has come under frequent attack.

One cause for concern is the extensive reliance on researcher judgment that is inherent in cluster analysis. Also troubling is the fact that, unlike techniques such as regression and variance analyses, cluster analysis does not offer a test statistic that provides a clear answer regarding the support or lack of support of a set of results for a hypothesis of interest (Barney et al. 1990; Meyer 1991). Another major concern is the perception that applications of cluster analysis have lacked an underlying theoretical rationale. Cluster analysis’ sorting ability is powerful enough that it will provide clusters even if no meaningful groups are embedded in a sample. In fact, cluster analysis has the potential not only to offer inaccurate depictions of the groupings in a sample but also to impose groupings where none exist (Barney et al. 1990;

Reger et al. 1993; Ketchen et al. 1996). In the 1990s some critics even referred to the use of cluster analysis as an embarrassment to strategic management and singled out cluster analysis as a methodological stigma (Ketchen et al. 1996).

Recognizing these views, measures suggested by methodology experts for improving the robustness of cluster analysis were deliberately applied in this study. Choosing the appropriate clustering algorithms, i.e. the rules or procedures followed to sort observations, is critical to the effective use of cluster analysis (Punj et al. 1983). There are two basic types of algorithms: hierarchical algorithms and non-hierarchical algorithms.

Hierarchical algorithms process through a series of steps that build a tree-like structure by either adding individual elements to (i.e. agglomerative) or deleting from (i.e. divisive) clusters. Whereas agglomerative methods initially view each observation as a separate cluster and then compile them into successively smaller number of groups, eventually putting all into one group, divisive methods follow the opposite approach, by putting all observations into one group initially, and the observations are divided into smaller groups until eventually each observations becomes a separate cluster. The researcher must decide what level of division is appropriate. Although the methods start at the opposite ends of the clustering process, the number of groups identified should be the same regardless of which one is used. The five most popular agglomerative algorithms are ‘single linkage’, ‘complete linkage’, ‘average linkage’, ‘centroid method’, and ‘Ward’s method’ (Hair 2006). The differences among them lie in the procedures used to calculate the distance between clusters and each has different systematic tendencies in the way it groups observations. Ward’s method was used in this study because it is best suited for studies where the number of observations in each cluster is expected to be approximately equal and without outliers (Ketchen et al. 1996).

The following problems are well known in the context of analyses based on hierarchical algorithms (Aldenderfer et al. 1984; Everitt et al. 2001). First, researchers often do not know the underlying structure of a sample in advance, making it difficult to select the appropriate algorithm. Second, hierarchical algorithms make only one pass through a data set, so poor

cluster assignments cannot be modified. Third, solutions are often unstable when cases are dropped, especially when a sample is small. This is particularly troublesome for research in strategic management where sample sizes are often small. Given all mentioned issues the confidence in the validity of a solution obtained using only hierarchical clustering algorithms is limited (Jardine et al. 1971). Therefore this study used the largest possible sample, and applied both hierarchical and non-hierarchical algorithms.

Non-hierarchical algorithms, also known as K-means or iterative methods, partition a data set into a pre-specified number of clusters. After initial cluster ‘centroids’ (the ‘center points’

of clusters along input variables) are selected, each observation is assigned to the group with the nearest ‘centroid’. As each new observation is allocated, the cluster ‘centroids’ are recomputed. Multiple passes are made through a data set to allow observations to change cluster membership based on their distance from the recomputed centroids. To arrive at an optimal solution the passes through a data set continue until no observations change in clusters (Anderberg 1973). Non-hierarchical algorithms offer two advantages over hierarchical methods. First, by allowing observations to switch cluster membership, nonhierarchical methods are less impacted by outlier elements. Although outliers can initially distort clusters, this is often corrected in subsequent passes as the observations switch cluster membership (Aldenderfer et al. 1984; Hair 2006). Second, by making multiple passes through the data, the final solution optimizes within-cluster homogeneity and between-cluster heterogeneity. This requires that the number of clusters be specified a priori. For this study this is problematic because the number of clusters was not known a priori.

A solution advocated by methodology experts is to use a two-stage procedure where a hierarchical algorithm is used to define the number of clusters and cluster centroids. These results then serve as the starting points for subsequent non-hierarchical clustering (Punj et al.

1983; Hair 2006). This procedure increases validity of solutions and the only cost is the extra time and effort required on the researchers’ part (Punj et al. 1983; Ketchen et al. 1996).

Although many strategic grouping studies ignored this guidance, the best solutions often are those obtained by using hierarchical and non-hierarchical methods in tandem.

This study uses the recommended procedure to increase validity. First, it applies a hierarchical clustering algorithm (i.e. Ward’s method, as mentioned above) to determine the numbers of clusters in the data sample. The basic procedure is to inspect a dendogram, a graph of the order that observations join clusters and the similarity of observations joined (Ketchen et al. 1996). A dendogram indicates clusters by relatively dense branches, and by showing agglomeration coefficients, notably incremental changes in the coefficient. Such reliance on interpretation requires that this method is used cautiously (Aldenderfer et al. 1984).

Theory and literature can serve as a non-statistical tool for determining the number of clusters, and comparison of emergent clusters with a typology based on theory can provide evidence regarding the typology’s descriptive validity (Ketchen et al. 1993; Hair 2006). Therefore this study also compares the findings with existing typologies and frameworks which were reviewed during the synthesis of PE related literature. Upon triangulation of the findings, a non-hierarchical clustering algorithm (i.e. K-means) was used to validate the results.

K-means is a heuristic algorithm. It seeks for solutions among all possible ones and there is no guarantee that the best will be found. It was recommended to run it multiple times with different starting conditions. In this study a set of different starting constellations has had been derived from multiple runs of the hierarchical clustering algorithms. Statistical tests with external variables for each run validated the degree of accurateness. The validation procedures will be presented in the following chapter.