Assessing Partial Measurement Invariance in Cross-Group, Longitudinal, Congruence, and Multilevel Organizational Studies: Introducing the MEI Package in R

Measurement equivalence/invariance (ME/I) is a prerequisite for cross-group comparisons when using survey data. Although popular structural equation modeling software programs, including Mplus and lavaan, enable tests of ME/I using simple commands, identifying noninvariant items when full ME/I is rejected is more challenging. This paper reviews current procedures for identifying noninvariant items, particularly when there are more than two groups. We recommend systematically rotating the reference items and conducting pairwise comparisons on the factor loadings estimated in the configural invariance model and the intercepts estimated in the metric invariance model. The results are then summarized with the list-and-delete method to identify sets of invariant items and clusters of invariant groups. A custom R package, MEI, is developed to implement our recommended procedures. With simple commands, MEI automatically conducts ME/I tests, identifies noninvariant items, and compares latent means with partial measurement invariance. This allows researchers to interpret cross-group comparison results more precisely. Finally, our procedures for testing ME/I from cross-group comparisons and the MEI package are extended to longitudinal studies with panel data, congruence studies with dyadic data, and multilevel studies with nested data.