Comparison of Measurement Invariance Testing using Penalized Likelihood and Maximum Likelihood Estimators:A Monte Carlo Simulation Study

Abstract

Invariance testing remains a widely used and important issue for social scientists. At its heart, assessment of factor invariance involves an examination of the suitability of a scale’s use across an entire population. Traditionally, invariance testing has been carried out using a Chi-square difference test in conjunction with multiple group confirmatory factor analysis. However, research has demonstrated that this approach can result in inflated Type I error rates, or findings of a lack of invariance when in fact invariance is present. As a result, statisticians and methodologists have been investigating alternative approaches to testing invariance, which control the Type I error rate without sacrificing much in terms of power. The current study investigated one such alternative, based on a penalized likelihood estimator. This estimator has been previously investigated in the context of fitting structural equation models, and found to perform well in terms of parameter estimation accuracy. Results of the current Monte Carlo simulation study found that the PLE approach is in fact promising in the context of invariance assessment. It was able to control the Type I error rate better than did the Chi-square test, and it exhibited power rates that were as good as or better than those of the Chi-square. Implications of these findings are discussed.