Dimensionality of Binary Items
Abstract
Four different approaches are used to asses the dimensionality of binary items. This is done using a population model to allow sampling of both items and people and provides for variation and control of important parameters. Consider indices of dimensionality based on the pattern of second factor loadings derived from simplex theory are also accurate under many combinations of parameters and are second in accuracy to Local Independence. These indices decrease in accuracy substantially at the highest level of factor correlations and the widest dispersion of item difficulties that we used. The fitting of a simplex R-matrix to observed intercorrelations of binary items provides high accuracy under a wide range of parameters, but becomes highly sensitive to the combination of a high level of factor correlations and a wide distribution of item difficulties. An increase in sample size produces no increase in accuracy in the most unfavorable combination of parameters. A quantitative index of the shape of the curve of successive Eigenvalues was used for matrices of phi coefficients, tetrachoric correlations, and variance-covariance matrices. None of these indices produced satisfactory accuracy except under most favorable combinations of parameters. The Eigenvalues of variance-covariance matrices provide a more accurate basis for a decision concerning dimensionality than tetrachoric correlations, which have been the statistics of choice. Factor analysis, Binary items.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 15, 1988
- Accession Number
- ADA203238
Entities
People
- Ledyard R. Tucker
- Lloyd G. Humphreys
- Mary A. Roznowski
Organizations
- University of Illinois Urbana–Champaign