The purpose of this study was to evaluate the robustness
of some linear factor analytic techniques to
violations of the linearity assumption by factoring
product-moment correlations computed from data conforming
to an extended, three-parameter logistic model
of item responding. Three factors were crossed to
yield 81 subcases: the number of underlying dimensions
(0, 1, or 2), the number of items (10, 15, 20,
25, 30, 35, 40, 45, or 50), and the number of subjects
(100, 250, or 500). The mean eigenvalues for the subcases
were evaluated using parallel analysis and the
scree technique. The mean eigenvectors were visually
inspected. For almost all subcases with one or two underlying
dimensions, a single spurious factor was able
to be identified using parallel analysis. However, in
comparison with the nonspurious factors, it was small
in magnitude and, in practice, factors of this relative
size might be interpreted as trivial. It was concluded
that researchers may have some confidence in interpreting
linear factor analysis with binary items if they
are using a test instrument that has been carefully developed.
Green, Samuel B. (1983). Identifiability of spurious factors using linear factor analysis with binary items. Applied Psychological Measurement, 7, 139-147. doi:10.1177/014662168300700202
Green, Samuel B..
Identifiability of spurious factors using linear factor analysis with binary items.
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