Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis

In studies of multiple groups of respondents, such as cross-national surveys and cross-cultural assessments in psychological or educational testing, an important methodological consideration is the comparability or "equivalence" of measurement across the groups. Ideally full equivalence would hold, but very often it does not. If nonequivalence of measurement is ignored when it is present, substantively interesting comparisons between the groups may become distorted. We consider this question in multigroup latent variable modeling of multiple-item scales, specifically latent trait models for categorical items. We use numerical sensitivity analyses to examine the nature and magnitude of the distortions in different circumstances, and the factors that affect them. The results suggest that estimates of multigroup latent variable models can be sensitive to assumptions about measurement, in that nonequivalence of measurement does not need to be extreme before ignoring it may substantially affect cross-group comparisons. We also discuss the implications of such findings on the analysis of large comparative studies.