Performing Cluster Analysis Within a Person-Oriented Context: Some Methods for Evaluating the Quality of Cluster Solutions

Abstract

The paper focuses on the internal validity of clustering solutions. The “goodness” of a cluster structure can be judged by means of different cluster quality coefficient (QC) measures, such as the percentage of explained variance, the point-biserial correlation, the Silhouette coefficient, etc. The paper presents the most commonly used QCs occurring in well-known statistical program packages, and we have strived to make the presentation as non technical as possible to make it accessible to the applied researcher. The focus is on QCs useful in person-oriented research. Based on simulated data with independent variables, the paper shows that QCs can be strongly influenced by the number of clusters and the number of input variables, and that the value of a QC can be fairly high even in the absence of any real cluster structure. When evaluating the internal validity, it is helpful to relate the QCs of a clustering solution to those obtained in parallel analyses of random data. We also introduce a new type of QC, measuring the relative improvement (MORI) of a QC obtained for a certain clustering solution relative to the corresponding QC based on a relevant type of random data.