Non-Equivalence of Measurement in Latent Variable Modelling of Multigroup Data : A Sensitivity Analysis

In cross-national surveys and other studies of multiple groups of respondents, 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 non-equivalence of measurement is ignored when it is present, substantively interesting comparisons between the groups may become biased. We consider such biases in multigroup latent variable modelling of multiple-item scales, specifically latent class and latent trait models for categorical items. We use numerical sensitivity analyses to examine the nature and magnitude of the biases in different circumstances. The results suggest that estimates of multigroup latent variable models can be sensitive to assumptions about measurement, in that non-equivalence of measurement does not need to be extreme before ignoring it may substantially distort cross-group comparisons. Some factors which affect the degree of this bias are described, and results for latent class and latent trait models are compared. We also discuss the implications of such findings on the analysis of large cross-national surveys and other comparative studies