International large-scale assessments (LSAs) such as the Programme for International Student Assessment (PISA) provide important information about the distribution of student proficiencies across a wide range of countries. The repeated assessments of these content domains offer policymakers important information for evaluating educational reforms and received considerable attention from the media. Furthermore, the analytical strategies employed in LSAs often define methodological standards for applied researchers in the field. Hence, it is vital to critically reflect the conceptual foundations of analytical choices in LSA studies. This article discusses methodological challenges in selecting and specifying the scaling model used to obtain proficiency estimates from the individual student responses in LSA studies. We distinguish design-based inference from model-based inference. It is argued that for the official reporting of LSA results, design-based inference should be preferred because it allows for a clear definition of the target of inference (e.g., country mean achievement) and is less sensitive to specific modeling assumptions. More specifically, we discuss five analytical choices in the specification of the scaling model: (1) Specification of the functional form of item response functions, (2) the treatment of local dependencies and multidimensionality, (3) the consideration of test-taking behavior for estimating student ability, and the role of country differential items functioning (DIF) for (4) cross-country comparisons, and (5) trend estimation. This article's primary goal is to stimulate discussion about recently implemented changes and suggested refinements of the scaling models in LSA studies.
An empirical characteristic scaling model for freely-propagating lean premixed hydrogen flames
