On Studying Common Factor Dominance and Approximate Unidimensionality in Multicomponent Measuring Instruments With Discrete Items.

This article outlines a procedure for examining the degree to which a common factor may be dominating additional factors in a multicomponent measuring instrument consisting of binary items. The procedure rests on an application of the latent variable modeling methodology and accounts for the discrete nature of the manifest indicators. The method provides point and interval estimates (a) of the proportion of the variance explained by all factors, which is due to the common (global) factor and (b) of the proportion of the variance explained by all factors, which is due to some or all other (local) factors. The discussed approach can also be readily used as a means of assessing approximate unidimensionality when considering application of unidimensional versus multidimensional item response modeling. The procedure is similarly utilizable in case of highly discrete (e.g., Likert-type) ordinal items, and is illustrated with a numerical example.