This simulation study investigated the empirical Type I error rates of using the maximum likelihood estimation method and Pearson covariance matrix for multi-group confirmatory factor analysis (MGCFA) of full and strong measurement invariance hypotheses with mixed item format data that are ordinal in nature. The results indicate that mixed item formats and sample size combinations do not result in inflated empirical Type I error rates for rejecting the true measurement invariance hypotheses. Therefore, although the common methods are in a sense sub-optimal, they don’t lead to researchers claiming that measures are functioning differently across groups – i.e., a lack of measurement invariance.
Koh, Kim H. and Zumbo, Bruno D.
"Multi-Group Confirmatory Factor Analysis for Testing Measurement Invariance in Mixed Item Format Data,"
Journal of Modern Applied Statistical Methods: Vol. 7
, Article 12.
Available at: http://digitalcommons.wayne.edu/jmasm/vol7/iss2/12