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A Monte Carlo Study of Constrained Factor Analysis Using Maximum Likelihood and Unweighted Least Squares

From each of 105 samples of 300 observations each and from each of 87 samples of 3,000 each, constrained factor analyses of 96 normally distributed variables arranged in a three-stage hierarchical structure were computed by maximum likelihood (ML) and unweighted least squares (ULS). It was evident that ULS not only takes less time and computer resources than does ML, but also leads to better estimates for small sample sizes. It was also evident that when a large number of variables are loaded highly on a factor, especially when those variables have high communalities, the adverse effects of small sample size are somewhat diminished. Finally, it was evident that the occurrence of a boundary problem does not necessarily detract from the overall validity of a solution.