Problems with parallel analysis in data sets with oblique simple structure

Parallel analysis, one of the most promising methods to determine the number of principal components or factors to retain (Velicer, Eaton, & Fava, 2000), has been shown to underestimate the number of components to retain when the first eigenvalue is large (Turner, 1998). In order to further explore the potential problems with parallel analysis, orthogonal and oblique 4-, 8-, and 12-component solutions with four different degrees of simple structure were computed for simulated data. Since the first eigenvalue of the oblique solutions was generally large, parallel analysis was expected to underestimate the number of components to retain in these solutions. This was confirmed in the present simulation study. Even in solutions with pronounced oblique simple structure, parallel analysis tended to result in underextraction for the 8- and 12-component solutions. Thus, one should be aware of the possibility of underextractions when parallel analysis is used with data yielding components or factors with oblique simple structure.