Conditional covariance-based nonparametric multidimensionality assessment

William Stout, Brian Habing, Jeff Douglas, Hae Rim Kim, Louis Roussos, Jinming Zhang

Research output: Contribution to journalArticlepeer-review


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 dimensionality assessment 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 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.

Original languageEnglish (US)
Pages (from-to)331-354
Number of pages24
JournalApplied Psychological Measurement
Issue number4
StatePublished - Dec 1996
Externally publishedYes


  • Approximate simple structure
  • Conditional covariance
  • Dimensionality
  • Hierarchical cluster analysis
  • IRT
  • Local independence
  • LSAT
  • Multidimensionality
  • Simple structure

ASJC Scopus subject areas

  • General Psychology
  • Psychology (miscellaneous)
  • Social Sciences (miscellaneous)


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