AUTHOR=Wen Congcong , Hu Feng 

TITLE=Investigating the Applicability of Alignment—A Monte Carlo Simulation Study

JOURNAL=Frontiers in Psychology

VOLUME=Volume 13 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2022.845721

DOI=10.3389/fpsyg.2022.845721

ISSN=1664-1078

ABSTRACT=Traditional multiple-group CFA is usually criticized for having too restrictive model assumption, namely the scalar measurement invariance. The new multiple-group analysis method, alignment evaluates measurement invariance and more importantly, permits factor mean comparisons without requiring scalar invariance which is usually required in traditional multiple-group CFA. 
Based on the simulation studies of Asparouhov and Muthén and of Flake and McCoach, this current simulation study is broken into three parts.
Study 1 shows that the acceptable noninvariance rates of alignment in three factor models range from 20% to 30% when the amounts of groups vary from three to 9,15,30. .Alignment can accept more large noninvariant parameters than small noninvariant ones. Alignment can also accept more noninvariant parameters when the amount of groups decreases from nine, 15 or 30 to three. 
Study 2 shows that when the model has no noninvariant parameters, the alignment requires relatively lower group sizes. Explicitly, the minimal group size required for alignment was 250 when the amount of groups was three, the minimal group size was 150 when the amount of groups was nine, and 200 when the amount of groups was 15. When there are noninvariant parameters in the model and the amount of groups is low, a group size of 350 is a safe rule of thumb. When there are noninvariant parameters in the model and the amount of groups is high, a group size of 250 is required for trustworthy results.
Study 3 shows that multiple-group CFA provides accurate factor mean estimates only when each factor had 20% factor loading (1 factor loading) with small-sized cross-loading. Multiple-group ESEM provides accurate factor mean estimates when the magnitude of cross-loading is small or when each factor had 20% factor loading (1 factor loading) with medium-sized cross-loading. Alignment provides accurate factor mean estimates when there are only small-sized cross-loadings in the model. Multiple-group CFA is more suitable for use when scalar invariance is established. Multiple-group ESEM works best when there are small-sized or only a few medium-sized cross-loadings in the model. Alignment can allow for small-sized cross-loadings and a few noninvariant parameters in the model.