Conditional Covariance-Based Nonparametric Multidimensionality Assessment

According to the weak local independence approach to defining dimensionality, the fundamental quantities for determining a test's dimensional structure are the co variances of item-pair responses conditioned on exam inee trait level. This paper describes three dimensionality assessment procedures-HCA/CCPROX, DIMTEST, and DETECT—that use estimates of these con ditional covariances. All three procedures are nonpara metric ; that is, they do not depend on the functional form of the item response functions. These procedures are applied to a dimensionality study of the LSAT, which illustrates the capacity of the approaches to assess the lack of unidimensionality, identify groups of items manifesting approximate simple structure, determine the number of dominant dimensions, and measure the amount of multidimensionality.