Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal…

In the literature of modern psychometric modeling, mostly related to item response theory (IRT), the fit of model is evaluated through known indices, such as X[superscript 2], M2, and root mean square error of approximation (RMSEA) for absolute assessments as well as Akaike information criterion (AIC), consistent AIC (CAIC), and Bayesian…

Based on the framework of testlet models, the current study suggests the Bayesian random block item response theory (BRB IRT) model to fit forced-choice formats where an item block is composed of three or more items. To account for local dependence among items within a block, the BRB IRT model incorporated a random block effect into the response…

Multilevel data are a reality for many disciplines. Currently, although multiple options exist for the treatment of multilevel data, most disciplines strictly adhere to one method for multilevel data regardless of the specific research design circumstances. The purpose of this Monte Carlo simulation study is to compare several methods for the…

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of…

There has been much controversy over the null hypothesis significance testing procedure, with much of the criticism centered on the problem of inverse inference. Specifically, p gives the probability of the finding (or one more extreme) given the null hypothesis, whereas the null hypothesis significance testing procedure involves drawing a…

The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of…

The multilevel latent class model (MLCM) is a multilevel extension of a latent class model (LCM) that is used to analyze nested structure data structure. The nonparametric version of an MLCM assumes a discrete latent variable at a higher-level nesting structure to account for the dependency among observations nested within a higher-level unit. In…

The present study investigates different approaches to adding covariates and the impact in fitting mixture item response theory models. Mixture item response theory models serve as an important methodology for tackling several psychometric issues in test development, including the detection of latent differential item functioning. A Monte Carlo…

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation…

Student Growth Percentiles (SGPs) increasingly are being used in the United States for inferences about student achievement growth and educator effectiveness. Emerging research has indicated that SGPs estimated from observed test scores have large measurement errors. As such, little is known about "true" SGPs, which are defined in terms…

Conventional differential item functioning (DIF) detection methods (e.g., the Mantel-Haenszel test) can be used to detect DIF only across observed groups, such as gender or ethnicity. However, research has found that DIF is not typically fully explained by an observed variable. True sources of DIF may include unobserved, latent variables, such as…

Traditional estimators of item response theory scale scores ignore uncertainty carried over from the item calibration process, which can lead to incorrect estimates of the standard errors of measurement (SEMs). Here, the authors review a variety of approaches that have been applied to this problem and compare them on the basis of their statistical…

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of…

Effects of dimensionality on ability estimation of an adaptive test were examined using generated data in Bayesian computerized adaptive testing (CAT) simulations. Generally, increasing interdimensional difficulty association produced a slight decrease in test length and an increase in accuracy of ability estimation as assessed by root mean square…