Using New Proximity Measures With Hierarchical Cluster Analysis to Detect Multidimensionality

A new approach for partitioning test items into dimensionally distinct item clusters is introduced. The core of the approach is a new item-pair conditional-covariancebased proximity measure that can be used with hierarchical cluster analysis. An extensive simulation study designed to test the limits of the approach indicates that when approximate simple structure holds, the procedure can correctly partition the test into dimensionally homogeneous item clusters even for very high correlations between the latent dimensions. In particular, the procedure can correctly classify (on average) over 90% of the items for correlations as high as .9. The cooperative role that the procedure can play when used in conjunction with other dimensionality assessment procedures is discussed. The increasing recognition of the multidimensional nature of educational and psychological measurement instruments has given rise to a concurrent increasing need for more efficient and more effective dimensionality assessment tools. In response to this need, this article deals with the development of a new dimensionality estimation tool based on the use of agglomerative hierarchical cluster analysis (HCA) with new dimensionally sensitive proximity measures. If successful HCA dimensionality methods can be developed such that clusters of items that appear to measure a common dimension can be located, then such methods will not only be useful by themselves, but will also be a valuable aid to existing procedures such as DIMTEST (Nandakumar & Stout, 1993; Stout, 1987), DETECT (Kim, 1994; Zhang & Stout, 1995, 1996), and nonlinear factor analysis. This is because all exploratory or confirmatory dimensionality analyses can benefit from beginning either with a single core set of dimensionally homogeneous items or with multiple sets of such items. The selection of such sets of items has been a very difficult problem in the history of dimensionality analysis, and the present article offers a potentially very effective solution. For example, in using DIMTEST to determine whether a test is unidimensional, the practitioner is required to identify one or more sets of items that are suspected of being dimensionally homogeneous; these are then tested for dimensional distinctiveness from the rest of the test. The clusters