According to the weak local independence approach
to defining dimensionality, the fundamental quantities
for determining a test’s dimensional structure are the covariances
of item-pair responses conditioned on examinee
trait level. This paper describes three
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 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. Index terms: approximate
simple structure, conditional covariance, DETECT,
dimensionality, DIMTEST, HCA/CCPROX,
hierarchical cluster analysis, IRT, LSAT, local independence, multidimensionality, simple structure.
Stout, William; Habing, Brian; Douglas, Jeff; Kim, Hae Rim; Roussos, Louis; Zhang, Jinming.
Conditional covariance-based nonparametric multidimensionality assessment.
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