A monte carlo investigation of three approaches to
assessing the dimensionality of binary items used a
population model that allowed sampling of items
and examinees and provided for variation and control
of important parameters. The model was
realistic of performance of binary items in current
tests of cognitive abilities. Three indices were investigated
: one based on the property of local independence
of unidimensional tests (the independence
index), one based on patterns of second factor
loadings derived from simplex theory (the pattern
index), and one that reflects the shape of the curve
of successive eigenvalues (the ratio of differences
index). The last index was used for matrices of phi
coefficients, tetrachoric correlations, and variances-covariances.
The local independence index reported
here was the most accurate dimensionality index.
The pattern index was accurate under many combinations
of parameters, but decreased substantially
at the highest level of factor correlations and the
widest dispersion of item difficulties. None of the
eigenvalue indices produced satisfactory accuracy,
except under the most favorable combinations of
parameters. Nonetheless, the eigenvalues of
variance-covariance matrices provided a more accurate
basis for dimensionality decisions than tetrachoric
correlations, which have been the statistic of
choice of many investigators. Recommendations
for use are also given. Index terms: binary items,
dimensionality, factor analysis, phi correlations,
Roznowski, Mary, Tucker, Ledyard R & Humphreys, Lloyd G. (1991). Three approaches to determining the dimensionality of binary items. Applied Psychological Measurement, 15, 109-127. doi:10.1177/014662169101500201
Roznowski, Mary; Tucker, Ledyard R.; Humphreys, Lloyd G..
Three approaches to determining the dimensionality of binary items.
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