Conditional covariance-based nonparametric multidimensionality assessment

According to the weak local independence approachto defining dimensionality, the fundamental quantitiesfor determining a test’s dimensional structure are the covariancesof item-pair responses conditioned on examineetrait level. This paper describes threedimensionality assessmentprocedures-HCA/CCPROX,DIMTEST, and DETECT-that use estimates of these conditionalcovariances. All three procedures are nonparametric; that is, they do not depend on the functionalform of the item response functions. These proceduresare applied to a dimensionality study of the LSAT, whichillustrates the capacity of the approaches to assess thelack of unidimensionality, identify groups of itemsmanifesting approximate simple structure, determine thenumber of dominant dimensions, and measure theamount of multidimensionality. Index terms: approximatesimple structure, conditional covariance, DETECT,dimensionality, DIMTEST, HCA/CCPROX,hierarchical cluster analysis, IRT, LSAT, local independence, multidimensionality, simple structure.