Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures (DPMs) offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT…

Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the…

Item compromise has long posed challenges in educational measurement, jeopardizing both test validity and test security of continuous tests. Detecting compromised items is therefore crucial to address this concern. The present literature on compromised item detection reveals two notable gaps: First, the majority of existing methods are based upon…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…

In standardized educational testing, test items are reused in multiple test administrations. To ensure the validity of test scores, the psychometric properties of items should remain unchanged over time. In this article, we consider the sequential monitoring of test items, in particular, the detection of abrupt changes to their psychometric…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a…

The Bayesian way of accounting for the effects of error in the ability and item parameters in adaptive testing is through the joint posterior distribution of all parameters. An optimized Markov chain Monte Carlo algorithm for adaptive testing is presented, which samples this distribution in real time to score the examinee's ability and optimally…

Parametric methods, such as autoregressive models or latent growth modeling, are usually inflexible to model the dependence and nonlinear effects among the changes of latent traits whenever the time gap is irregular and the recorded time points are individually varying. Often in practice, the growth trend of latent traits is subject to certain…

For surveys of complex issues that entail multiple steps, multiple reference points, and nongradient attributes (e.g., social inequality), this study proposes a new multiprocess model that integrates ideal-point and dominance approaches into a treelike structure (IDtree). In the IDtree, an ideal-point approach describes an individual's attitude…

A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on…

The modern web-based technology greatly popularizes computer-administered testing, also known as online testing. When these online tests are administered continuously within a certain "testing window," many items are likely to be exposed and compromised, posing a type of test security concern. In addition, if the testing time is limited,…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

Calibration of new items online has been an important topic in item replenishment for multidimensional computerized adaptive testing (MCAT). Several online calibration methods have been proposed for MCAT, such as multidimensional "one expectation-maximization (EM) cycle" (M-OEM) and multidimensional "multiple EM cycles"…