Application of multivariate Rasch models in international large-scale educational assessments

In large-scale educational assessments, such as the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS), a primary concern is with the estimation of the population-level characteristics of a number of latent variables and the relationships between latent variables and other variables. Typically these studies are undertaken in contexts in which there are constraints on sample size and individual student response time, yet there are high expectations with regard to the breadth of content coverage. These demands and constraints have resulted in such studies using rotated-booklet designs, with each student responding to a limited number of items on each of a number of scales. This paper describes the techniques that have been employed in such studies to enable the reliable estimation of population characteristics when there is considerable unreliability at the student level. It also discusses the methodology that is used to make the data sets produced in such studies amenable for use by data analysts undertaking secondary analyses using standard analytic too.