Princilpal cluster component analysis revisited

To construct a scale consisting of multiple sum scores based on item responses, we formulated a constrained Principal Component Analysis (PCA) that produces exclusive and exhaustive clusters of items. By replacing the loadings of each item with a single regression coefficient and zeros, the loading matrix is transformed into a perfect simple structure. This method reduces to a non-hierarchical clustering of variables, where the sum of the largest eigenvalues of correlation matrices for clusters is maximized, which is equivalent to the Principal Cluster Component Analysis (PCCA) developed in the 1970 s but not widely known. This straightforward method yields solutions comparable to more recently developed, sophisticated methods. PCCA performed better for defining sum scores with maximum coefficient \(\alpha\) $\alpha$ than the common procedure using Exploratory Factor Analysis (EFA) when analyzing a real data set.