ANALYSIS OF LATENT DIMENSIONALITY OF DICHOTOMOUSLY AND POLYTOMOUSLY SCORED TEST DATA
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概要
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Three closely related latent space dimensionality assessment procedures are surveyed. They are DIMTEST (called POLY-DIMTEST in the polytomous case), HCA/ PROX, and DETECT. Each procedure works for both dichotomous and polytomous scoring. These procedures form a conceptual unity because they all estimate item pair conditional covariances given latent ability. As such, they are nonparametric and weak local independence based procedures. DIMTEST assesses for dichotomously scored items whether a test's latent space is unidimensional or not. POLY-DIMTEST does the same for polytomously scored items. HCA/PROX does a hierarchical cluster analysis of items based on the Roussos dimensionality-sensitive proximity measure, thereby searching for item clusters that are dimensionally homogeneous within cluster and heterogeneous between clusters. When such approximate simple structure holds, DIMTEST is used in conjunction with HCA/PROX to identify which level of the HCA/ PROX cluster partition hierarchy best describes the multidimensional simple structure driving the data. DETECT, with the aide of Zhang's genetic algorithm based optimization procedure, counts the number of dominant dimensions, measures the size of the departure from unidimensionality, and searches for dimensionally homogeneous item clusters when approximate simple structure holds. All three procedures are described and judged effective based on a blend of simulation studies and real data analyses, using studies in the literature as well as some studies reported herein. Finally, an overview of some work in progress is given. This includes enhancements of the above procedures as well as some new procedures.
- 日本行動計量学会の論文
日本行動計量学会 | 論文
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