“…Similar conclusions were obtained from studies targeting design-based correction procedures applied in the 2012 Programme for International Student Assessment (PISA) data. In these studies, design-based corrections did not always result in scalar invariance (e.g., Marksteiner et al, 2019), and the relations with the criterion (i.e., achievement) differed between uncorrected and corrected scores (e.g., Vonkova, Papajoanu, et al, 2018). One limitation of this work is that each correction procedure was independently assessed, with the assumption that such corrections operate on data from all respondents to the same extent.…”