The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

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…

This study evaluates various scoring methods including number-correct scoring, IRT theta scoring, and hybrid scoring in terms of scale-score stability over time. A simulation study was conducted to examine the relative performance of five scoring methods in terms of preserving the first two moments of scale scores for a population in a chain of…

We develop a structural after measurement (SAM) method for structural equation models (SEMs) that accommodates missing data. The results show that the proposed SAM missing data estimator outperforms conventional full information (FI) estimators in terms of convergence, bias, and root-mean-square-error in small-to-moderate samples or large samples…

The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

Synthesizing findings about the indirect (mediated) effect plays an important role in determining the mechanism through which variables affect one another. This simulation study compared six methods for synthesizing indirect effects: correlation-based MASEM, parameter-based MASEM, marginal likelihood synthesis, an adjustment to marginal likelihood…

The computerized adaptive tests (CAT) apply an adaptive process in which the items are tailored to individuals' ability scores. The multidimensional CAT (MCAT) designs differ in terms of different item selection, ability estimation, and termination methods being used. This study aims at investigating the performance of the MCAT designs used to…

Weighted least squares (WLS), weighted least squares mean-and-variance-adjusted (WLSMV), unweighted least squares mean-and-variance-adjusted (ULSMV), maximum likelihood (ML), robust maximum likelihood (MLR) and Bayesian estimation methods were compared in mixed item response type data via Monte Carlo simulation. The percentage of polytomous items,…

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…

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

The purpose of the present study is to apply the item response theory (IRT) and testlet response theory (TRT) models to a reading comprehension test. This study applied the TRT models and the traditional IRT model to a seventh-grade reading comprehension test (n = 8,815) with eight testlets. These three models were compared to determine the best…

Bayesian statistical approaches to mixed treatment comparisons (MTCs) are becoming more popular because of their flexibility and interpretability. Many randomized clinical trials report multiple outcomes with possible inherent correlations. Moreover, MTC data are typically sparse (although richer than standard meta-analysis, comparing only two…

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…

The purpose of this inquiry was to investigate the effectiveness of item response theory (IRT) proficiency estimators in terms of estimation bias and error under multistage testing (MST). We chose a 2-stage MST design in which 1 adaptation to the examinees' ability levels takes place. It includes 4 modules (1 at Stage 1, 3 at Stage 2) and 3 paths…

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…