Assessing the Measurement Equivalence of a set of Items: Item-specific Diagnostics on an Interpretable Metric

The characteristic of `measuring the same thing repeatedly in the same way' makes psychological tests with equivalent items an attractive choice for one-off assessments and progress monitoring. A hierarchy of factor analysis measurement models formalizes the global equivalence of the item set. The traditional model comparison approach provides a binary statistical significance decision about the global level of equivalence, but interpretable local diagnostics to assess the degree of equivalence for specific items on a meaningful metric are not yet available. We introduce such item-specific effect-size diagnostics through smart use of the effect-coding identification rule to set the to-be-measured latent variable’s scale.