Large-scale international assessments rely on indicators of the resources that students report having in their homes to capture the financial capital of their families. The scaling methodology currently used to develop the Programme for International Student Assessment (PISA) background indices is designed to maximize within-country comparability…

Item-level information, such as difficulty and discrimination are invaluable to the test assembly, equating, and scoring practices. Estimating these parameters within the context of large-scale performance assessments is often hindered by the use of unbalanced designs for assigning examinees to tasks and raters because such designs result in very…