Determining the number of dimensions is extremely important in applying item response theory (IRT) models to data. Traditional and revised parallel analyses have been proposed within the factor analysis framework, and both have shown some promise in assessing dimensionality. However, their performance in the IRT framework has not been…

To reduce the chance of Heywood cases or nonconvergence in estimating the 2PL or the 3PL model in the marginal maximum likelihood with the expectation-maximization (MML-EM) estimation method, priors for the item slope parameter in the 2PL model or for the pseudo-guessing parameter in the 3PL model can be used and the marginal maximum a posteriori…

This research examined correlation estimates between latent abilities when using the two-dimensional and three-dimensional compensatory and noncompensatory item response theory models. Simulation study results showed that the recovery of the latent correlation was best when the test contained 100% of simple structure items for all models and…

The unstructured multiple-attempt (MA) item response data in virtual learning environments (VLEs) are often from student-selected assessment data sets, which include missing data, single-attempt responses, multiple-attempt responses, and unknown growth ability across attempts, leading to a complex and complicated scenario for using this kind of…

In this study, we propose aggregating test scores with unidimensional within-test structure and multidimensional across-test structure based on a 2-level, 1-factor model. In particular, we compare 6 score aggregation methods: average of standardized test raw scores (M1), regression factor score estimate of the 1-factor model based on the…

Cognitive diagnosis models provide profile information about a set of latent binary attributes, whereas item response models yield a summary report on a latent continuous trait. To utilize the advantages of both models, higher order cognitive diagnosis models were developed in which information about both latent binary attributes and latent…

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

Educational and psychological constructs are normally measured by multifaceted dimensions. The measured construct is defined and measured by a set of related subdomains. A bifactor model can accurately describe such data with both the measured construct and the related subdomains. However, a limitation of the bifactor model is the orthogonality…

An automated item selection procedure in Mokken scale analysis partitions a set of items into one or more Mokken scales, if the data allow. Two algorithms are available that pursue the same goal of selecting Mokken scales of maximum length: Mokken's original automated item selection procedure (AISP) and a genetic algorithm (GA). Minimum…

This simulation study compared the performances (Type I error and power) of Mantel-Haenszel (MH), SIBTEST, and item response theory-likelihood ratio (IRT-LR) methods under certain conditions. Manipulated factors were sample size, ability differences between groups, test length, the percentage of differential item functioning (DIF), and underlying…

The random-threshold generalized unfolding model (RTGUM) was developed by treating the thresholds in the generalized unfolding model as random effects rather than fixed effects to account for the subjective nature of the selection of categories in Likert items. The parameters of the new model can be estimated with the JAGS (Just Another Gibbs…

This dissertation proposes two modified cognitive diagnostic models (CDMs), the deterministic, inputs, noisy, "and" gate with hierarchy (DINA-H) model and the deterministic, inputs, noisy, "or" gate with hierarchy (DINO-H) model. Both models incorporate the hierarchical structures of the cognitive skills in the model estimation…

Content balancing is one of the most important components in the computerized adaptive testing (CAT) especially in the K to 12 large scale tests that complex constraint structure is required to cover a broad spectrum of content. The purpose of this study is to compare the weighted penalty model (WPM) and the weighted deviation method (WDM) under…

In this study we examined procedures for assessing model-data fit of item response theory (IRT) models for mixed format data. The model fit indices used in this study include PARSCALE's G[superscript 2], Orlando and Thissen's S-X[superscript 2] and S-G[superscript 2], and Stone's chi[superscript 2*] and G[superscript 2*]. To investigate the…