Assessment of dimensionality in dichotomously-scored data using multidimensional scaling.

Persistent Link:
http://hdl.handle.net/10150/184267
Title:
Assessment of dimensionality in dichotomously-scored data using multidimensional scaling.
Author:
Jones, Patricia Ann Blodgett.
Issue Date:
1987
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The effectiveness of multidimensional scaling (MDS) techniques in recovering the underlying dimensionality of dichotomously-scored data was examined for unidimensional and multidimensional data. Thirty-three data sets of varying numbers of dimensions with differing patterns of item discrimination were generated using a multidimensional latent trait model in a Monte Carlo simulation study. Margin-sensitive measures (agreement, phi, and kappa) and margin-free measures (Φ/ Φ(max), Yule's Q, and the tetrachoric correlation) were used as measures of similarity and the resulting matrices were scaled in one through five dimensions. Values of the stress coefficient, S₁, S₁ by dimensionality plots, and plot configurations were examined to determine the dimensionality of the item set. Principal components analyses (PCAs) of phi and tetrachoric matrices were carried out as a basis for comparison. In addition, MDS and PCA were used to examine a data set comprised of items obtained from the routing tests of the Head Start Measures Battery. Two effects of item discrimination on MDS results were especially noteworthy. First, factors tended to be located equally distant from each other in the MDS space. Items were located closest to the factor for which the primary factor loading occurred. Second, as item discrimination decreased, items tended to be more widely dispersed from their appropriate locations in space. Extra dimensions in the MDS representational space were required for margin-sensitive coefficients to accommodate difficulty effects. Margin-free coefficients generally eliminated difficulty-related dimensions, although occasional problems were noted with the tetrachoric correlation. Analysis of the HSMB revealed that the data were primarily unidimensional, although specific effects due to each subtest were clearly present in the analysis. MDS was found to be a useful technique and its use in conjunction with PCA or factor analysis is recommended.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Multidimensional scaling.; Item response theory.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Educational Foundations and Administration; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Sabers

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAssessment of dimensionality in dichotomously-scored data using multidimensional scaling.en_US
dc.creatorJones, Patricia Ann Blodgett.en_US
dc.contributor.authorJones, Patricia Ann Blodgett.en_US
dc.date.issued1987en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe effectiveness of multidimensional scaling (MDS) techniques in recovering the underlying dimensionality of dichotomously-scored data was examined for unidimensional and multidimensional data. Thirty-three data sets of varying numbers of dimensions with differing patterns of item discrimination were generated using a multidimensional latent trait model in a Monte Carlo simulation study. Margin-sensitive measures (agreement, phi, and kappa) and margin-free measures (Φ/ Φ(max), Yule's Q, and the tetrachoric correlation) were used as measures of similarity and the resulting matrices were scaled in one through five dimensions. Values of the stress coefficient, S₁, S₁ by dimensionality plots, and plot configurations were examined to determine the dimensionality of the item set. Principal components analyses (PCAs) of phi and tetrachoric matrices were carried out as a basis for comparison. In addition, MDS and PCA were used to examine a data set comprised of items obtained from the routing tests of the Head Start Measures Battery. Two effects of item discrimination on MDS results were especially noteworthy. First, factors tended to be located equally distant from each other in the MDS space. Items were located closest to the factor for which the primary factor loading occurred. Second, as item discrimination decreased, items tended to be more widely dispersed from their appropriate locations in space. Extra dimensions in the MDS representational space were required for margin-sensitive coefficients to accommodate difficulty effects. Margin-free coefficients generally eliminated difficulty-related dimensions, although occasional problems were noted with the tetrachoric correlation. Analysis of the HSMB revealed that the data were primarily unidimensional, although specific effects due to each subtest were clearly present in the analysis. MDS was found to be a useful technique and its use in conjunction with PCA or factor analysis is recommended.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMultidimensional scaling.en_US
dc.subjectItem response theory.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineEducational Foundations and Administrationen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorSabersen_US
dc.identifier.proquest8804177en_US
dc.identifier.oclc700056151en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.