So, now that we have gone through the effort of learning about the different extraction methods and figuring how to run them in SAS, what difference do they really make? Let’s see by comparing the results of five different extraction methods using the data sets summarized in Example data sets. We ran these models using the same syntax presented in the section above, just changing the METHOD option and eliminating the PR IORS option for all except the PAF and iterated PAF methods. We then organized the results into some nice summary tables to permit easy comparison.

Engineering data. As we mentioned above, this data usually gives a clear two-factor solution. Communality estimates for the engineering data across different extraction techniques presents the communality estimates for the initial extraction, and each of the subsequent extraction methods. As you can see, the communalities for the various items are relatively stable despite the relatively small sample size, rarely varying by more than 0.10 across all extraction methods for a particular item. Eigenvalues extracted for the engineering data across different extraction techniques presents the eigenvalues extracted by the various methods. We also see very similar eigenvalues produced across the various methods. This suggests that when basic assumptions are met and factor structure is clear, the extraction method might not matter much.

Self-description questionnaire data. As in the previous analysis, you can see that analyses of the SDQ by various extraction methods produce relatively similar results regardless of the extraction method. The communalities extracted were similar, and the eigenvalues were also similar (presented in Communality estimates for the SDQ data across different extraction techniques and Eigenvalues extracted for the SDQ data across different extraction techniques). These results further support the conclusion that extraction method is of little importance when basic assumptions are met and factor structure is clear.

GDS data. The goal of the third analysis is to compare the results of various extraction techniques on data with less clarity of structure. Because this data is binary (0, 1 values only) it is likely that it does not meet the assumption of multivariate normality. If one takes the advice above seriously, iterated PAF or ULS should be used given the non-normal data. As you can see in Comparison of communalities across extraction methods, the iterated PAF and ULS methods yield nearly identical results. The remaining methods differ, with substantial differences in communalities extracted for several variables in the scale. (See highlighted rows.) Comparing ML to iterated PAF and ULS, it is clear that the recommendation to use iterated PAF or ULS when data is not multivariate normal should be seriously considered. There are also some items in Comparison of communalities across extraction methods that exhibited substantial discrepancies between ML and iterated PAF or ULS (for example, see GDS01 or GDS12).

The initial iterated PAF extraction did not converge on a solution within the default number of iterations (25). This can indicate there is a problem with the data or analysis that is causing the estimates to be volatile and not converge on a solution. In this instance, the maximum number of iterations (MAXITER) was increased and a solution was converged upon at iteration 60. Since the iterated PAF results mimic those of the ULS extraction, we can conclude that there was not a problem with the analysis or results, but that ULS extraction might reach a solution faster than iterated PAF extraction.

The eigenvalues extracted also vary dramatically across extraction methods, as you can see in Comparison of extracted eigenvalues for different extraction techniques. Once again, ML produces the most unexpected results, but iterated PAF and ULS results are probably the most reliable. Note that ML produced smaller eigenvalues for the first factor than the second factor, which is unusual but is merely a reflection of the relatively extreme loadings produced.