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Assessing Dimensionality by Maximizing 'H' Coefficient-Based Objective Functions

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Title: Assessing Dimensionality by Maximizing 'H' Coefficient-Based Objective Functions
Language: English
Authors: van Abswoude, Alexandra A. H., Vermunt, Jeroen K., Hemker, Bas T.
Source: Applied Psychological Measurement. 2007 31(4):308-330.
Availability: SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: http://sagepub.com
Peer Reviewed: Y
Physical Description: PDF
Page Count: 23
Publication Date: 2007
Document Type: Journal Articles
Reports - Evaluative
Descriptors: Measures (Individuals), Probability, Simulation, Item Response Theory, Models, Mathematics, Sample Size
DOI: 10.1177/0146621606295196
ISSN: 0146-6216
Abstract: Mokken scale analysis can be used for scaling under nonparametric item response theory models. The results may, however, not reflect the underlying dimensionality of data. Various features of Mokken scale analysis--the H coefficient, Mokken scale conditions, and algorithms--may explain this result. In this article, three new H-based objective functions with slight reformulations of Mokken scale analysis in the unidimensional and multidimensional cases are introduced. Deterministic and stochastic nonhierarchical clustering algorithms reduced the probability of obtaining suboptimal solutions. A simulation study investigated whether these methods can determine the dimensionality structure of data sets that vary with respect to item discrimination, item difficulty, number of items per trait, and numbers of observations per test. Furthermore, it was investigated whether deterministic and stochastic algorithms can generate approximately global optimal solutions. The method based on the average within-scale H[subscript i] combined with a stochastic nonhierarchical clustering algorithm was the most successful in dimensionality assessment. (Contains 7 tables, 2 figures and 1 note.)
Abstractor: Author
Number of References: 37
Entry Date: 2007
Accession Number: EJ767189
Database: ERIC
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  Data: Mokken scale analysis can be used for scaling under nonparametric item response theory models. The results may, however, not reflect the underlying dimensionality of data. Various features of Mokken scale analysis--the H coefficient, Mokken scale conditions, and algorithms--may explain this result. In this article, three new H-based objective functions with slight reformulations of Mokken scale analysis in the unidimensional and multidimensional cases are introduced. Deterministic and stochastic nonhierarchical clustering algorithms reduced the probability of obtaining suboptimal solutions. A simulation study investigated whether these methods can determine the dimensionality structure of data sets that vary with respect to item discrimination, item difficulty, number of items per trait, and numbers of observations per test. Furthermore, it was investigated whether deterministic and stochastic algorithms can generate approximately global optimal solutions. The method based on the average within-scale H[subscript i] combined with a stochastic nonhierarchical clustering algorithm was the most successful in dimensionality assessment. (Contains 7 tables, 2 figures and 1 note.)
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