Among current state-of-art estimation methods for multilevel IRT models, the two-stage divide-and-conquer strategy has practical advantages, such as clearer definition of factors, convenience for secondary data analysis, convenience for model calibration and fit evaluation, and avoidance of improper solutions. However, various studies have shown…

This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test…

The current study introduced a general modeling framework, multilevel mixture IRT (MMIRT) which detects and describes characteristics of population heterogeneity, while accommodating the hierarchical data structure. In addition to introducing both continuous and discrete approaches to MMIRT, the main focus of the current study was to distinguish…

In a pretest-posttest cluster-randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores that ignores measurement error in the…

Students' interest in science declines in secondary school. Therefore, motivating students to become competent and engaged in science topics that are relevant for their everyday lives is an important goal, so they can be better citizens and decision makers with socioscientific issues (e.g., climate change and waste disposal). The present study…

We investigated methods of including covariates in two-level models for cluster randomized trials to increase power to detect the treatment effect. We compared multilevel models that included either an observed cluster mean or a latent cluster mean as a covariate, as well as the effect of including Level 1 deviation scores in the model. A Monte…

The current study applied the person-fit statistic, l[subscript z], to data from a Canadian provincial achievement test to explore the usefulness of conducting person-fit analysis on large-scale assessments. Item parameter estimates were compared before and after the misfitting student responses, as identified by l[subscript z], were removed. The…

This study examines the use of cross-classified random effects models (CCrem) and cross-classified multiple membership random effects models (CCMMrem) to model rater bias and estimate teacher effectiveness. Effect estimates are compared using CTT versus item response theory (IRT) scaling methods and three models (i.e., conventional multilevel…

This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE)…

Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…

Alternatives to vertical scales are compared for measuring longitudinal academic growth and for producing school-level growth measures. The alternatives examined were empirical cross-grade regression, ordinary least squares and logistic regression, and multilevel models. The student data used for the comparisons were Arabic Grades 4 to 10 in…

Measuring and linking competencies require special instruments, special data collection designs, and special statistical models. The measurement instruments are tests or tests forms, which can be used in the following situations: The same test can be given repeatedly; two or more parallel tests forms (i.e., forms intended to be similar in…

Large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) sample examinees to whom an exam will be administered. In most situations the sampling design is not a simple random sample and must be accounted for in the estimating model. After reviewing the current operational estimation procedure for NAEP, this…