A Correlation-Based Decision-Rule for Determining the Number of Clusters and Its Efficiency in Uni- and Multi-Level Data

In this article two versions of a decision-rule (SDC1 , 2) for determining the most appropriate number of clusters on the basis of a correlation matrix are presented, applied, and compared with three other decision rules: (a) Kaiser's eigenvalue greater than one (EV), (b) the scree test (ST), and (c) Horn's parallel analysis (PA). The new decision-rule is based on the sums of disaggregate correlations for definite cluster solutions. All decision-rules are applied to correlation matrices with a uni-level or a multi-level structure. Multi-level data include a surface level and a deep level. In uni-level data four of the five rules are quite efficient. In multi-level data one version of the new decision-rule (SDC2,) is most efficient in determining the number of clusters on the surface level. Three of the other decision-rules (SDC1, EV, ST) are also efficient on the surface level. In contrast, the PA rule shows efficiency on the deep level but not on the surface level. An empirical example towards the end of this article will support this finding.