Extension procedures for confirmatory factor analysis

We present factor extension procedures for confirmatory factor analysis that provide estimates of the relations of common and unique factors with external variables that do not undergo factor analysis. We present identification strategies that build upon restrictions of the pattern of correlations between unique factors and external variables. The first restriction minimizes the sum of squared correlations between unique factors and external variables. This approach is similar to the traditional factor extension procedure. The second restriction minimizes the complexity of the pattern of external correlations of unique factors. This approach has similarities with the simple structure ideal imposed on most factor rotation strategies. The procedures are illustrated with a real data example that demonstrates their applicability to real-world research questions.