A New Method to Interpret Cluster Analysis Results in the Presence of Heterogeneous Clusters

Abstract

Contrary to several other statistical analyses (ANOVA, linear regression, etc.) normality is not a requirement of cluster analysis (CA). However, certain types of departure from normality, such as high skewness, can cause problems in CAs. In such cases the proportion of extreme cases will increase, increasing the chance to obtain heterogeneous clusters. The aim of the paper is to propose a new method for interpreting CA results in the presence of heterogeneous clusters. After performing CA, all cases are classified as either typical or atypical, depending on how close they are to their own cluster center (cluster centroid). A key concept is a new variable that measures the distance of each case to its own cluster centroid. A case is considered typical if this distance does not exceed a predetermined threshold, and atypical if it does. Typical cases can be used to provide a robust estimation of the cluster centroids. Additionally, analyzing subgroups of atypical cases within clusters where they reach an interpretable proportion can refine the explanation of cluster profile. The usefulness of the new method is demonstrated using four parental attachment variables of avoidance and anxiety, where high skewness and therefore heterogeneous clusters are anticipated. The study sample consisted of 918 young adults aged between 20 and 35. Standard hierarchical and k-means clustering analysis identified a 6-cluster structure as the best solution, yielding easily interpretable parental attachment types. The proportion of atypical cases exceeded 5% in three clusters. The psychological meaning of these clusters could be explored in more detail by computing cluster centroids based on typical cases and then comparing groups of typical and atypical cases using Welch’s t-tests. The new method can easily be applied in the Validation module of the latest version of the ROPstat software. The parental attachment styles explored were comparable to those found in literature.