We compared the fit of the higher-order factor and blended variable models to the two BFAS data sets reported by DeYoung et al. (2007)
and to a third BFAS data set obtained for the purpose of this article. The first data set consisted of 481 adults of the Eugene-Springfield (Oregon) community sample, and the second consisted of 480 university students in Ontario (see DeYoung et al., 2007
, for details of these participant samples). The third data set consisted of 230 university students in Alberta (68% women, median age 20 years). Appendix A
shows the correlations and descriptive statistics for the BFAS variables in the Alberta sample.
Before comparing the higher-order factor and blended variable models, we began with a baseline model in which all five factors were constrained to be orthogonal, and in which each factor was defined only by its two constituent aspect scales, which were constrained to have equal loadings. To define the higher-order factor model, we modified the original model to include two correlated higher-order factors, alpha and beta, that influence the lower-order factors. Specifically, we allowed the Emotional Stability (i.e., low Neuroticism), Agreeableness, and Conscientiousness factors to load on a higher-order alpha factor. We also allowed the Extraversion and Openness to Experience factors to load on a higher-order beta factor, with the loadings on beta constrained to be equal. We allowed the alpha and beta factors to correlate.
To define the blended variable model, we modified the baseline model to allow five secondary loadings on the basis of modification indices obtained from the Oregon sample. Specifically, we selected the first path with the largest modification index obtained from the baseline model, and then selected the second path with the largest modification index obtained from the model with the first secondary path added. This procedure continued until five secondary loadings had been added to the original model. As a result, we allowed five secondary loadings of BFAS variables as follows: (low) Withdrawal, Industriousness, and Intellect on Extraversion, Enthusiasm on Agreeableness, and Politeness on Conscientiousness. The model with these secondary loadings was evaluated in the Ontario and Alberta samples as well as in the Oregon sample, which served as the derivation sample.
We should note that our aim in these analyses was to compare the relative levels of fit for the competing models, and not simply to produce more complex models that will have particularly high absolute levels of fit. Absolute levels of fit are expected to be rather poor, for two reasons. First, because the personality domain is not characterized by true simple structure, most of the facet-level variables would show appreciable secondary loadings on one or more factors. Also, some pairs of aspects from different Big Five factors might reflect some areas of similar (or opposite) content not accounted for by the five large factors, with the result that there will be some residual correlations among those facets. But because our aim in this article is simply to compare the levels of fit for the higher-order factor and blended variable models, we did not attempt to incorporate these various additional sources of covariance within the models below.
We conducted confirmatory factor analyses conducted using AMOS 7.0 using maximum likelihood estimation, and we evaluated model fit in terms of the SRMR and RMSEA indices (Hu & Bentler, 1999). Figures , , and show the results for the baseline model and the two competing models as applied to the BFAS in the three participant samples. In all three samples, the fit of the baseline model (i.e., orthogonal factors, no secondary loadings) was exceeded by that of the higher-order factor model (ΔSRMR = .05, .07, and .04, and ΔRMSEA = .01, .02, and .01, for the Oregon, Ontario, and Alberta samples, respectively) and by that of the blended variable model (ΔSRMR = .08, .08, and .07, and ΔRMSEA = .06, .05, and .05, for the Oregon, Ontario, and Alberta samples, respectively). Regarding the differences between the higher-order and blended models, all fit indices favored the blended variable model over the higher-order factor model (ΔSRMR = .03, .01, and .03, and ΔRMSEA = .06, .04, and .05, for the Oregon, Ontario, and Alberta samples, respectively). Moreover, all three samples showed no overlap in the 90% confidence intervals for the RMSEA values. We should note that the superior fit for the blended model was observed not only in the Oregon sample (i.e., the derivation sample), but also in the Ontario and Alberta samples (i.e., the validation samples). These results indicate that the higher-order factor model clearly has no advantage over the blended variable model in approximating the correlations among the 10 BFAS variables. On the contrary, the blended variable model provided a substantially better approximation than did the higher-order factor model.4
Original Model Applied to 10 Big Five Aspect Scales
Higher-Order Factor Model Applied to 10 Big Five Aspect Scales
Blended Variable Model Applied to 10 Big Five Aspect Scales