Assessing measurement invariance of ordinal indicators in cross-national research

Cross-national comparability of the WHOQOL-BREF: A measurement invariance approach

“…In order to account for multiple testing, a Bonferroni correction was applied, and the critical p-value is set at .002. As such, items 5,6,7,10,11,15,16,17,18,19, and 26 are found to fail threshold invariance.…”

“…An alternative would be to make subtle modifications to the model (for example adding cross-loadings on the basis of the modification indices; see [11]) to increase the model fit, but this route was not pursued, because all 24 facet items are clearly designed to measure one and only one domain, which would make cross-loadings meaningless from a substantive point of view.…”

“…Consequently, because the items of the WHO-QOL-BREF are ordinal, an estimation method that explicitly takes this ordinality into account was used (more precisely, the Weighted Least Squares estimator with a mean-and variance-adjusted Chi-square (WLSMV) on a polychoric correlation matrix along with the Delta parameterization in Mplus [11,13]). Apart from selecting an appropriate estimation method, conducting a multigroup CFA with ordinal indicators requires a specialized approach.…”

“…Items marked with *do not have equal thresholds across groups (i.e., a statistical significant Dv 2 ). Reference items are in bold For item 24, three instead of four thresholds are estimated, because the fifth response category is never selected 1 The following constraints were applied in order to identify the model (see [11]): (1) the latent factor means are fixed to 0 in the first group, (2) the intercepts are fixed to 0 in all groups, (3) the scaling factors are fixed to one in the first group, (4) per factor, the factor loading of one item is fixed to 1 (these items are called the reference items), and (5) for each item, an equality constraint was set on the first threshold, and additionally for the reference items, the second threshold was also constrained across groups.…”

“…Data analysis Measurement invariance is tested using multi-group confirmatory factor analysis (CFA), which is not robust against violating the assumption of continuous factor indicators [11,12]. Consequently, because the items of the WHO-QOL-BREF are ordinal, an estimation method that explicitly takes this ordinality into account was used (more precisely, the Weighted Least Squares estimator with a mean-and variance-adjusted Chi-square (WLSMV) on a polychoric correlation matrix along with the Delta parameterization in Mplus [11,13]).…”