Finding Clusters of Measurement Invariant Items for Continuous Covariates

Measurement invariance (MI) cannot always be achieved for the full length of a test or questionnaire, leading researchers to seek for measurement invariant item subsets. Previous approaches either 1) can only analyze group covariates or 2) make implicit assumptions on the nature of MI and then yield a single item set. We provide a general approach for identifying invariant item sets via structural equation modeling that can be applied to dichotomous as well as continuous covariates. It yields multiple item clusters of close measurement invariant items and gives researchers comprehensive insight into the non-MI structure of a test. Furthermore, it allows making well-justified decisions on their assumptions when inferring on group differences or relationships with other variables. The proposed approach performed well in an extensive simulation study. We illustrate the usage and merits of the approach with empirical data on mood states.