Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores

This paper explores the insight from the application of cluster analysis to the results of a Data Envelopment Analysis of productive behaviour. Cluster analysis involves the identification of groups among a set of different objects (individuals or characteristics). This is done via the definitions of a distance matrix that defines the relationship between the different objects, which then allows the determination of which objects are most similar into clusters. In the case of DEA, cluster analysis methods can be used to determine the degree of sensitivity of the efficiency score for a particular DMU to the presence of the other DMUs in the sample that make up the reference technology to that DMU. Using the bootstrapped values of the efficiency measures we construct two types of distance matrices. One is defined as a function of the variance covariance matrix of the scores with respect to each other. This implies that the covariance of the score of one DMU is used as a measure of the degree to which the efficiency measure for a single DMU is influenced by the efficiency level of another. An alternative distance measure is defined as a function of the ranks of the bootstrapped efficiency. An example is provided using both measures as the clustering distance for both a one input one output case and a two input two output case.