Comparing results of an exact vs. an approximate (Bayesian) measurement invariance test: a cross-country illustration with a scale to measure 19 human values

One of the most frequently used procedures for measurement invariance testing is the multigroup confirmatory factor analysis (MGCFA). Muthén and Asparouhov recently proposed a new approach to test for approximate rather than exact measurement invariance using Bayesian MGCFA. Approximate measurement invariance permits small differences between parameters otherwise constrained to be equal in the classical exact approach. However, extant knowledge about how results of approximate measurement invariance tests compare to the results of the exact measurement invariance test is missing. We address this gap by comparing the results of exact and approximate cross-country measurement invariance tests of a revised scale to measure human values. Several studies that measured basic human values with the Portrait Values Questionnaire (PVQ) reported problems of measurement noninvariance (especially scalar noninvariance) across countries. Recently Schwartz et al. proposed a refined value theory and an instrument (PVQ-5X) to measure 19 more narrowly defined values. Cieciuch et al. tested its measurement invariance properties across eight countries and established exact scalar measurement invariance for 10 of the 19 values. The current study applied the approximate measurement invariance procedure on the same data and established approximate scalar measurement invariance even for all 19 values. Thus, the first conclusion is that the approximate approach provides more encouraging results for the usefulness of the scale for cross-cultural research, although this finding needs to be generalized and validated in future research using population data. The second conclusion is that the approximate measurement invariance is more likely than the exact approach to establish measurement invariance, although further simulation studies are needed to determine more precise recommendations about how large the permissible variance of the priors may be.