The purpose of this study is to demonstrate clustering methods within a functional data analysis (FDA) framework for identifying subgroups of individuals that may be exhibiting categories of misfit. Person response functions (PRFs) estimated within a FDA framework (FDA-PRFs) provide graphical displays that can aid in the identification of persons…

The purpose of this study is to illustrate the use of functional data analysis (FDA) as a general methodology for analyzing person response functions (PRFs). Applications of FDA to psychometrics have included the estimation of item response functions and latent distributions, as well as differential item functioning. Although FDA has been…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

Trends in International Mathematics and Science Study (TIMSS) is an international comparative study designed to measure trends in mathematics and science achievement at grades 4 and 8, as well as to collect information about educational contexts (such as students' schools, teachers, and homes) that may be related to student achievement. TIMSS has…

Science literacy, which is included in Programme for International Student Assessment (PISA) as an assessment area, is an important research and discussion area of science education literature with all its dimensions. In this study, the clustering results of the students from 34 Organization for Economic Cooperation and Development (OECD)…

We introduce an approach for making a quantitative comparison of the item response curves (IRCs) of any two populations on a multiple-choice test instrument. In this study, we employ simulated and actual data. We apply our approach to a dataset of 12,187 participants on the 25-item Science Literacy Concept Inventory (SLCI), which includes ample…

Large-scale assessments (LSAs) use Mislevy's "plausible value" (PV) approach to relate student proficiency to noncognitive variables administered in a background questionnaire. This method requires background variables to be completely observed, a requirement that is seldom fulfilled. In this article, we evaluate and compare the…

The OECD's PISA exercise has by now been widely critiqued. Whilst we agree with most concerns, we begin with the assumption that PISA will remain an enduring and powerful feature of the global educational landscape. Even if the PISA test itself were discontinued, a similar large-scale quantitative assessment exercise would soon arise to take its…