| Developments in multidimensional item response theory (MIRT) have increased the development of dimensionality tools to assess the dimensional structure of item pools. This study investigated the comparative effectiveness of the hierarchical cluster analyses (HCA) when using nonparametric and parametric proximity measures for identifying the dimensional structure of data. The nonparametric approach is based on the assumption that the patterns of local independence in the conditional covariances can yield information about the dimensional structure, while the parametric approach is based on the angular distance (direction cosines) converted from direction estimated multidimensional discrimination parameter estimates.;Simulation studies were designed to determine if item difficulty, guessing, and ability levels influence the correct classifications of two approaches under various conditions. Different proximity measures, HCAs, sample sizes, number of clusters, test length, and dimensional structures (approximate independent [APSS] and mixed structure [MS]) were considered as simulation factors.;Major findings of the study were: (1) CA using nonparametric similarity measures (especially the average method) were successful (higher than 90% recovery) for the APSS, but not successful for the MS. (2) CA using parametric similarity measures (especially Ward's method) were successful for both the APSS and the MS. (3) While difficulty and guessing levels did not affect the clustering results, ability levels (especially at lower ability) influenced the clustering results.;Since Ward's method with the angular distance yielded stable classifications under various test conditions, the parametric approach is recommended for analyzing the structure of test content. Wise use of proposed parametric and nonparametric approaches together can provide useful information about the dimensional structure. Because both methods work well with large sample sizes, they are useful for large-scale assessments such as standardized achievement/attitude tests. Caution should be used when a test is measuring relatively large number of diverse traits with small numbers of items related to each of them. |
