New Procedure for Extension Analysis in Exploratory Factor Analysis

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Abstract
Exploratory common factors have been correlated with variables external to the factor analysis by either extension analysis estimates or by correlating the external variables with estimated factor scores. In item analysis, a set of such correlations with possible scales is often computed for final item selection. The purposes of the present article are to document a problem common to both methods of estimating such correlations and to propose a new method of extension analysis that avoids this problem with less restriction assumptions. Solutions for a common data set by all three methods of extension analysis are presented that show the expected difficulties and improvements in the results. Because the new extension procedure gives the correlations without using estimated factor scores, use of this extension procedure eliminates factor indeterminacy from the multiple ways to estimate common factor scores. This method of evaluating possible scales was shown to have advantages over item-remainder correlational analysis.