International Large Scale Assessments have been producing data about educational attainment for over 60 years. More recently however, these assessments as tests have become digitally and computationally complex and increasingly rely on the calculative work performed by algorithms. In this article I first consider the coordination of relations…

The vertical scales of large-scale achievement tests created by using item response theory (IRT) models are mostly based on cluster (or correlated) educational data in which students usually are clustered in certain groups or settings (classrooms or schools). While such application directly violated assumption of independent sample of person in…