Detecting Correlated Residuals in Exploratory Factor Analysis: New Proposals and a Comparison of Procedures

In the classical exploratory factor analysis (EFA) model, residuals are constrained to be uncorrelated. However, since the 1960s, extensions of the classical model that allow correlated residuals to be modeled exist. Furthermore, in many EFA applications (especially those intended for item analysis) it is highly relevant to decide whether an extended solution is more appropriate than the simpler classical solution. This decision, in turn, requires effective and powerful methods for detecting correlated residuals (doublets) when they are really present to be available. This paper discusses two existing detection approaches in the EFA context, and proposes a third, new procedure. Reference values, based on the concept of parallel analysis, are proposed for deciding the relevance of the flagged doublets in all the considered procedures. The functioning of the three procedures is assessed by using simulation, and illustrated with an illustrative example. The proposal, finally, has been implemented in a well-known noncommercial EFA program, and an implementation in R is being developed.