Testing and Explaining Differences in Common and Residual Factors Across Many Countries

To make valid comparisons across countries, a measurement instrument needs to be measurement invariant across countries. The present article provides a nontechnical exposition of a recently proposed multilevel factor analysis approach to test measurement invariance across countries. It is explained that strong factorial invariance across countries implies equal factor loadings across levels and zero residual variance at the country level in a two-level factor model. Using two-level factor analysis, the decomposition of the variance at each level can be investigated, measurement invariance can be tested, and country-level variables can be added to explain differences in the common or residual factors. The approach is illustrated using two examples. The first example features data about well-being from the European Social Survey and the second example uses data about mathematical ability from the Programme for International Student Assessment (PISA) study. The input-files and annotated output-files for both examples are provided in the supplementary files.