Comparing Results of an Exact Versus an Approximate (Bayesian) Measurement Invariance Test: A Cross-Country Illustration with a New Scale to Measure 19 Human Values

Abstract

One of the most frequently used procedures for measurement invariance testing is the multigroup confirmatory factor analysis (MGCFA). Muthén and Asparouhov (2013) 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 results of exact versus approximate (Bayesian) cross-country measurement invariance tests of the 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 (e.g., Davidov, Schmidt, Schwartz, 2008). Schwartz et al. (2012) proposed a refined value theory and an instrument (PVQ-5X) to measure 19 more narrowly defined values. Cieciuch, Davidov, Vecchione, Beierlein and Schwartz (2014) tested its measurement invariance properties across eight countries and showed that the PVQ-5X is substantially more cross-country invariant than the old PVQ version to measure 10 values. They established exact scalar measurement invariance for 10 values. The current study applied the approximate measurement invariance and established approximate scalar measurement invariance even for all 19 values.

Keywords: multigroup confirmatory factor analysis, exact measurement invariance, approximate measurement invariance, configural metric scalar measurement invariance, Revised Portrait Values Questionnaire, Bayesian analysis