CONDITIONAL COVARIANCE-BASED NONPARAMETRIC MULTIDIMENSIONALITY ASSESSMENT

According to the weak local independence approach to defining dimensio nality, the fundamental quantities for determining a test's dimensiona l structure are the covariances of item-pair responses conditioned on examinee trait level. This paper describes three dimensionality assess ment procedures-HCA/CCPROX, DIMTEST, and DETECT-that use estimates of these conditional covariances. All three procedures are nonparametric; that is, they do not depend on the functional form of the item respon se functions. These procedures are applied to a dimensionality study o f the LSAT, which illustrates the capacity of the approaches to assess the lack of unidimensionality, identify groups of items manifesting a pproximate simple structure, determine the number of dominant dimensio ns, and measure the amount of multidimensionality.