Generating correlation matrices with model error for simulation studies in factor analysis: a combination of the Tucker-Koopman-Linn model and Wijsman's algorithm.

Most simulation studies in factor analysis follow a process of constructing population correlation matrices from the common-factor model and generating sample correlation matrices from the population matrices. In the common-factor model, the population correlation matrix is perfectly fit by the model's containing common and unique factors. However, since no mathematical model accounts exactly for the real-world phenomena that it is intended to represent, the Tucker-Koopman-Linn model (1969) is more realistic for generating correlation matrices than the conventional common-factor model because the former incorporates model error. In this paper, a procedure for generating population and sample correlation matrices with model error by combining the Tucker-Koopman-Linn model and Wijsman's algorithm (1959) is presented. The SAS/IML program for generating correlation matrices is described, and an example is also provided.