We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

This research aims to compare the ability and item parameter estimations of Item Response Theory according to Maximum likelihood and Bayesian approaches in different Monte Carlo simulation conditions. For this purpose, depending on the changes in the priori distribution type, sample size, test length, and logistics model, the ability and item…

Forced-choice (FC) measures have been widely used in many personality or attitude tests as an alternative to rating scales, which employ comparative rather than absolute judgments. Several response biases, such as social desirability, response styles, and acquiescence bias, can be reduced effectively. Another type of data linked with comparative…

Computerized Adaptive Testing (CAT) is a beneficial test technique that decreases the number of items that need to be administered by taking items in accordance with individuals' own ability levels. After the CAT applications were constructed based on the unidimensional Item Response Theory (IRT), Multidimensional CAT (MCAT) applications have…

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the…

A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the…

In this digital ITEMS module, Dr. Brian Leventhal and Dr. Allison Ames provide an overview of "Monte Carlo simulation studies" (MCSS) in "item response theory" (IRT). MCSS are utilized for a variety of reasons, one of the most compelling being that they can be used when analytic solutions are impractical or nonexistent because…

Longitudinal models of individual growth typically emphasize between-person predictors of change but ignore how growth may vary "within" persons because each person contributes only one point at each time to the model. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift…

Longitudinal models typically emphasize between-person predictors of change but ignore how growth varies "within" persons because each person contributes only one data point at each time. In contrast, modeling growth with multi-item assessments allows evaluation of how relative item performance may shift over time. While traditionally…

This dissertation informed researchers about the performance of different level-specific and target-specific model fit indices in Multilevel Latent Growth Model (MLGM) using unbalanced design and different trajectories. As the use of MLGMs is a relatively new field, this study helped further the field by informing researchers interested in using…

Data simulation and Monte Carlo simulation studies are important skills for researchers and practitioners of educational and psychological measurement, but there are few resources on the topic specific to item response theory. Even fewer resources exist on the statistical software techniques to implement simulation studies. This article presents…

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…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

When testing a statistical mediation model, it is assumed that factorial measurement invariance holds for the mediating construct across levels of the independent variable X. The consequences of failing to address the violations of measurement invariance in mediation models are largely unknown. The purpose of the present study was to…

In applications of item response theory (IRT), an estimate of the reliability of the ability estimates or sum scores is often reported. However, analytical expressions for the standard errors of the estimators of the reliability coefficients are not available in the literature and therefore the variability associated with the estimated reliability…