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,…

This dissertation aims to investigate the effect size measures of differential item functioning (DIF) detection in the context of cognitive diagnostic models (CDMs). A variety of DIF detection techniques have been developed in the context of CDMs. However, most of the DIF detection procedures focus on the null hypothesis significance test. Few…

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…

This rejoinder keeps the original focus on statistical computing pertaining to the correlation of student achievement between mathematics and science from the Trend in Mathematics and Science Study (TIMSS). Albeit the availability of student performance data in TIMSS and the emphasis of the inter-subject connection in the Next Generation Science…

Item response theory (IRT) has so many advantages than its precedent Classical Test Theory (CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not…

International large-scale assessments of student achievement such as International Association for the Evaluation of Educational Achievement's Trends in International Mathematics and Science Study (TIMSS) and Progress in International Reading Literacy Study and Organization for Economic Cooperation and Development's Program for International…

Purpose: Studies in the literature have generally demonstrated that the causes of differential item functioning (DIF) are complex and not directly related to defined groups. The purpose of this study is to determine the DIF according to the mixture item response theory (MixIRT) model, based on the latent group approach, as well as the…

This research empirically evaluates data sets from the National Center for Education Statistics (NCES) for design effects of ignoring the sampling design in weighted two-level analyses. Currently, researchers may ignore the sampling design beyond the levels that they model which might result in incorrect inferences regarding hypotheses due to…

This article combines statistical and applied research perspective showing problems that might arise when measurement error in multilevel compositional effects analysis is ignored. This article focuses on data where independent variables are constructed measures. Simulation studies are conducted evaluating methods that could overcome the…

Trend estimation in international comparative large-scale assessments relies on measurement invariance between countries. However, cross-national differential item functioning (DIF) has been repeatedly documented. We ran a simulation study using national item parameters, which required trends to be computed separately for each country, to compare…

Background: When studying student performance across different countries or cultures, an important aspect for comparisons is that of score comparability. In other words, it is imperative that the latent variable (i.e., construct of interest) is understood and measured equivalently across all participating groups or countries, if our inferences…

Socioeconomic status (SES) is often used as control variable when relations between academic outcomes and students' migrational background are investigated. When measuring SES, indicators used must have the same meaning across groups. This study aims to examine the measurement invariance of SES, using data from TIMSS, 2003. The study shows that a…

Stanford education professor Martin Carnoy examines four main critiques of how international test results are used in policymaking. Of particular interest are critiques of the policy analyses published by the Program for International Student Assessment (PISA). Using average PISA scores as a comparative measure of student achievement is misleading…