Enoch O. Oladunmoye

Measurement Invariance Across Groups: Connecting Confirmatory Factor Analytic and Item Response Theory Perspectives

Comparisons of psychological scores across groups, cultures, languages or occasions are interpretable only if the instrument measures the same construct in the same way in each. This note reviews measurement invariance as formulated in the confirmatory factor analytic (CFA) tradition and differential item functioning (DIF) as formulated in the item response theory (IRT) tradition, and sets out how the two can be combined in one staged workflow. It defines configural, metric, scalar (threshold) and strict invariance, explains why the level required depends on the intended comparison, and summarises current guidance on fit criteria, ordinal indicators, partial invariance, approximate invariance, alignment and Bayesian methods. It then describes the mathematical correspondence between ordinal CFA and the graded response model, and argues that the two traditions share a common model family and differ mainly in parameterisation, testing strategy and emphasis. Illustrative computations based on hypothetical item parameters show how uniform and non-uniform DIF alter item response functions, and how group-specific test information and conditional standard errors can reveal differences in precision that invariance tests alone do not. A seven-stage workflow, a table of common pitfalls and a reporting checklist are proposed. The workflow is a synthesis and has not been validated empirically; priorities for simulation and applied research are identified.