Evaluation of a new k-means approach for exploratory clustering of items

For the exploratory analysis of survey data commonly the exploratory factor analysis (EFA) is used. However, EFA is known to exhibit some problems. The major mathematical issue is the factor indeterminacy. Further problems are for example its weak performance in small sample sizes (n ≤ 150) and with high cross-loadings (e.g. Guadagnoli & Velicer, 1988; Sass, 2010; Wayne F. Velicer & Fava, 1998) as well as the general issue of the underlying measurement model including uncorrelated residual variances, what may be difficult to justify (Cudeck & Henly, 1991; MacCallum & Tucker, 1991; R. C. Tryon, 1959). The authors suggest two new k-means approaches as an alternative: k-means scaled distance measure (sdm) where items are represented in a coordinate system in a way so that their distance is based on one minus their correlation; and k-means cor where item inter-correlations are directly taken as the coordinate points of the items. These approaches were tested in a resampling with two real data sets and a traditional Monte Carlo simulation, as well as in a cross validation using confirmatory factor analysis (CFA). For dimensionality assessment the cluster validity coefficient Silhouette was used. In either analysis these approaches were compared to existing cluster analysis approaches and EFA. The authors conclude that the main advantage of the new approaches are (a) that cluster scores are determinate and (b) for item assignment kmeans sdm obtains better results than EFA and other cluster analysis approaches. The authors therefor suggest to use a combination of EFA methods for dimensionality assessment and kmeans for item assignment.