Overcoming Limitations of the Independent Clusters Model for CFA by Means of Bayes-Estimation and Buffered Simple Structure

The model of buffered simple structure is discussed as a method for modeling cross-loadings in confirmatory factor analysis. This method introduces assumptions from item sampling theory into confirmatory factor analysis. The independent clusters model, buffered simple structure, and Bayes estimation were compared by means of a simulation study based on three different population types. Population type A had zero cross-loadings, population type B had symmetrically distributed nonzero cross-loadings, and population type C had asymmetrically distributed nonzero cross-loadings. It turned out for population A that, although the independent clusters model yields the best loading estimate, it did not outperform Bayes estimation and buffered simple structure with respect to the factor inter-correlation estimate and model fit. One reason for this unexpected result could be that the specification of zero-cross loadings is suboptimal even when only sampling error introduces some cross-loadings. For populations B and C Bayes estimation and buffered simple structure clearly outperformed the independent clusters model. Overall, the results indicate that depending on the structure of cross-loadings in the population and depending on the focus on loading estimates or factor inter-correlation estimates, different modeling approaches might be appropriate.