Identification of Facet Models by Means of Factor Rotation: A Simulation Study and Data Analysis of a Test for the...

We investigated by means of a simulation study how well methods for factor rotation can identify a two-facet simple structure. Samples were generated from orthogonal and oblique two-facet population factor models with 4 (2 factors per facet) to 12 factors (6 factors per facet). Samples drawn from orthogonal populations were submitted to factor analysis with subsequent Varimax, Equamax, Parsimax, Factor Parsimony, Tandem I, Tandem II, Infomax, and McCammon's minimum entropy rotation. Samples drawn from oblique populations were submitted to factor analysis with subsequent Geomin rotation and a Promax-based Tandem II rotation. As a benchmark, we investigated a target rotation of the sample loadings toward the corresponding faceted population loadings. The three conditions were sample size (n = 400, 1,000), number of factors (q = 4-12), and main loading size (l = .40, .50, .60). For less than six orthogonal factors Infomax and McCammon's minimum entropy rotation and for six and more factors Tandem II rotation yielded the highest congruence of sample loading matrices with faceted population loading matrices. For six and more oblique factors Geomin rotation and a Promax-based Tandem II rotation yielded the highest congruence with faceted population loadings. Analysis of data of 393 participants that performed a test for the Berlin Model of Intelligence Structure revealed that the faceted structure of this model could be identified by means of a Promax-based Tandem II rotation of task aggregates corresponding to the cross-products of the facets. Implications for the identification of faceted models by means of factor rotation are discussed.