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,…

Despite broad applications of growth curve models, few studies have dealt with a practical issue -- nonnormality of data. Previous studies have used Student's "t" distributions to remedy the nonnormal problems. In this study, robust distributional growth curve models are proposed from a semiparametric Bayesian perspective, in which…

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…

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…

The purpose of this research is to first estimate the item and ability parameters and the standard error values related to those parameters obtained from Unidimensional Item Response Theory (UIRT), bifactor (BIF) and Testlet Response Theory models (TRT) in the tests including testlets, when the number of testlets, number of independent items, and…

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…

Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…

The purpose of the present study was to extend the model of measurement invariance by simultaneously estimating invariance across multiple populations in the dichotomous instrument case using multi-group confirmatory factor analytic and multiple indicator multiple causes (MIMIC) methodologies. Using the Arabic version of the General Aptitude Test…

In this paper, we document a study that involved applying a multiple imputation technique with chained equations to data drawn from the 2007 iteration of the TIMSS database. More precisely, we imputed missing variables contained in the student background datafile for Tunisia (one of the TIMSS 2007 participating countries), by using Van Buuren,…

Classroom context and climate are inherently classroom-level (L2) constructs, but applied researchers sometimes--inappropriately--represent them by student-level (L1) responses in single-level models rather than more appropriate multilevel models. Here we focus on important conceptual issues (distinctions between climate and contextual variables;…

The modeling of longitudinal and multilevel data using a latent variable framework is reviewed. Particular emphasis is placed on growth modeling. Examples are discussed where repeated observations are made on students sampled within classrooms and schools. The concept of a latent variable is a convenient way to represent statistical variation not…