Factor recovery by principal axis factoring and maximum likelihood factor analysis as a function of factor pattern and sample size

Abstract

Principal axis factoring (PAF) and maximum likelihood factor analysis (MLFA) are two of the most popular estimation methods in exploratory factor analysis. It is known that PAF is better able to recover weak factors and that the maximum likelihood estimator is asymptotically efficient. However, there is almost no evidence regarding which method should be preferred for different types of factor patterns and sample sizes. Simulations were conducted to investigate factor recovery by PAF and MLFA for distortions of ideal simple structure and sample sizes between 25 and 5000. Results showed that PAF is preferred for population solutions with few indicators per factor and for overextraction. MLFA outperformed PAF in cases of unequal loadings within factors and for underextraction. It was further shown that PAF and MLFA do not always converge with increasing sample size. The simulation findings were confirmed by an empirical study as well as by a classic plasmode, Thurstone's box problem. The present results are of practical value for factor analysts.