The Extra-Factor Phenomenon Revisited: Unidimensional Unfolding as Quadratic Factor Analysis

Abstract

The application of linear factor analysis to a set of unfoldable (unidimensional) items produces a two-dimensional solution, called the extra-factor phenomenon, which potentially results in incorrect conclusions about the nature of a set of items (van Schuur& Kiers, 1994). Many explanations have been offered for this phenomenon. This study attempted further clarification within the general theory of factor analysis. Specifically, it was demonstrated that the extra-factor phenomenon arises because: (1) the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model; and (2) at the level of covariance structure, the unidimensional quadratic factor model is not distinguishable from the two-dimensional linear factor model (McDonald, 1967). Also discussed are a number of theoretical linkages and bases of distinguishability that exist between unidimensional unfolding and linear factor analysis.