Confirmatory factor analytic procedures for the determination of measurement invariance

Confirmatory factor analytic (CFA) procedures can be used to provide evidence of measurement invariance. However, empirical evaluation has not focused on the accuracy of common CFA steps used to detect a lack of invariance across groups. This investigation examined procedures for detection of test structure differences across groups under several conditions through simulation. Specifically, sample size, number of factors, number of indicators per factor, and the distribution of the observed variables were manipulated, and 3 criteria for assessing measurement invariance were evaluated. Power and Type I error were examined to evaluate the accuracy of detecting a lack of invariance. Results suggest that the chi-square difference test adequately controls the Type I error rate in nearly all conditions, and provides relatively high power when used with maximum likelihood (ML) estimation and normally distributed observed variables. In addition, the power of the test to detect group differences for dichotomous observed variables with robust weighted least squares estimation was generally very low.