Identifiability of spurious factors using linear factor analysis with binary items

Abstract

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.