This study proposes a copula-based model that relaxes the multivariate normality assumption among latent traits in the joint modeling of multimodal data, such as item response and response times. In the structural model, the joint distribution of latent traits is defined via a copula with tail dependence. An expectation–maximization algorithm with stochastic approximation is implemented for parameter estimation. A simulation study evaluates the proposed method’s accuracy in ability estimation under various conditions, comparing it to traditional approaches. By better capturing the dependence structure between latent ability and speed, the proposed method outperforms the traditional approach with multivariate normality assumption. Applied to a variety of empirical datasets, the proposed method’s flexibility and the improvement in model fit are illustrated. The copula-based latent variable modeling can be generalized to broader applications in psychological testing involving multivariate latent traits.

Pfadt et al. present accessible methods for estimating conditional standard errors of measurement (CSEMs) and implement them in the open-source software JASP. Their emphasis on individual-level precision represents an important contribution to applied measurement practice. This commentary discusses several conceptual issues that clarify and extend the authors’ treatment of dimensionality, error definition, and score interpretation. The aim is to strengthen alignment between CSEM estimation and the interpretive purposes for which test scores are used.

We propose a latent trait model for the responses and response times on tests that separates capability from persistence. Core of the model is a race between a diffusion process and a censoring process. The diffusion process represents item-level cognitive processing and determines the processing time of a test taker. The censoring process sets the maximal time a test taker is willing to invest into an item. If the processing time is shorter than the maximal time, the response is generated by the diffusion process; otherwise, the response is generated differently. In the first version of the model, the response is generated by a random guess. In the second version of the model, the response is determined by the actual level of the diffusion process. We relate the diffusion process to the capability and response caution of a test taker and the censoring process to his willingness to invest time. Similar to models for rapid guessing, the proposed models take account of disengaged responding, but allow for individual differences in persistence and informed guessing. The model also provides a mathematical specification of persistence. In a simulation study, we investigate model fitting by marginal maximum likelihood estimation. We also apply the model to two empirical data sets.

Violations of the assumption of local independence are a fundamental issue in item response theory as they threaten model validity and bias the parameter estimates. For such a reason, a plethora of tests and approaches has been devised in the last 40 years to detect or to model such violations. Nonetheless, local dependence (LD) remains an open problem, with somewhat blurred boundaries due to the lack of a general framework for dealing with the different notions of dependence that have been suggested in the literature. The present contribution has a two-fold aim: On the one hand, to review and collect some of the approaches available in the literature; on the other hand, by following a unified perspective on assessment models introduced by Noventa et al. (2024, Journal of Mathematical Psychology 122, 102872) to suggest a possible systematization of some existing and some new approaches to LD. As a result, deterministic and probabilistic modeling mechanisms of LD are formalized and discussed.

ShinyItemAnalysis (SIA) is an R package and shiny application for an interactive presentation of psychometric methods and analysis of multi-item measurements in psychology, education, and social sciences in general. In this article, we present a new feature introduced in the recent version of the package, called “SIA modules,” which allows researchers and practitioners to offer new analytical methods for broader use via add-on extensions. SIA modules are designed to integrate with and build upon the SIA interactive application, enabling them to leverage the existing infrastructure for tasks, such as data uploading and processing. They can access and further use a range of outputs from various analyses, including models and datasets. Because SIA modules come in R packages (or extend existing ones), they can be bundled with their datasets, utilize object-oriented systems, or even compiled code. We illustrate the concepts using sample modules from the newly introduced SIAmodules package and other packages. After providing a general overview of building Shiny applications, we describe how to develop the SIA add-on modules with the support of the new SIAtools package. Finally, we discuss the possibilities of future development and emphasize the importance of freely available, interactive psychometric software for disseminating methodological innovations.

In latent space item response models (LSIRMs), subjects and items are embedded in a low-dimensional Euclidean latent space. As such, interactions among persons and/or items can be revealed that are unmodeled in conventional item response theory models. Current estimation approach for LSIRMs is a fully Bayesian procedure with Markov Chain Monte Carlo, which is, while practical, computationally challenging, hampering applied researchers to use the models in a wide range of settings. Therefore, we propose an LSIRM based on two variants of regularized joint maximum likelihood (JML) estimation: penalized JML and constrained JML. Owing to the absence of integrals in the likelihood, the JML methods allow for various models to be fit in limited amount of time. This computational speed facilitates a practical extension of LSIRMs to ordinal data, and the possibility to select the dimensionality of the latent space using cross-validation. In this study, we derive the two JML approaches and address different issues that arise when using maximum likelihood to estimate the LSIRM. We present a simulation study demonstrating acceptable parameter recovery and adequate performance of the cross-validation procedure. In addition, we estimate different binary and ordinal LSIRMs on real datasets pertaining to deductive reasoning and personality. All methods are implemented in R package ‘LSMjml’ which is available from CRAN.

The article proposes a new approach to estimating the latent distribution of item response theory (IRT) using kernel density estimation (KDE), particularly the solve-the-equation (STE) algorithm developed by Sheather and Jones (1991). As with existing methods, the KDE method aims to estimate the latent distribution of IRT to reduce biases in parameter estimates when the normality assumption on the latent variable is violated. Simulation studies and an empirical example confirm the robustness of algorithmic convergence of the KDE approach, and show that the KDE approach yields parameter estimates that are more accurate than or comparable to existing methods. Unlike other approaches that require multiple model fits for smoothing parameter selection, KDE requires only a single model-fitting step, substantially reducing computation time. These findings highlight KDE as a practical and efficient method for estimating latent distributions in IRT.

Traditional large-scale educational data are typically static and updated periodically, making it difficult to capture the dynamic changes in real time. However, recent technological advancements allow online exam platforms to collect students’ response data in real time. While item response theory (IRT) estimation methods are widely recognized for their accuracy, they are primarily designed for offline environments. When real-time data continuously arrives and online parameter estimation is required, these methods become computationally impractical. To address this challenge, we propose a recursive stochastic algorithm, i.e., truncated average stochastic Newton algorithm (TASNA), for the efficient online parameter estimation within the IRT framework. This algorithm significantly improves computational efficiency compared to the expectation–maximization (EM) algorithm implemented in the mirt package in R. The algorithm offers a powerful alternative to the traditional offline EM method. Furthermore, we investigate the asymptotic properties of the algorithm, proving its almost sure convergence and asymptotic normality. Numerical experiments using both simulated and real data demonstrate the practicality of the proposed method.

Multiple response (MR) items—such as multiple true-false, multiple-select, and select-N items—are increasingly used in assessments to identify partial knowledge and differentiate latent abilities more accurately. Allowing multiple selections, MR items provide richer information and reduce guessing effects compared to single-answer multiple-choice items. However, traditional scoring methods (e.g., Dichotomous, Ripkey, Partial scoring) compress response combination (RC) data, losing valuable information and ignoring issues like local dependence and incompatibility across item types. To address these challenges, we introduce a novel psychometric model framework: the Multiple Response Model with Inter-option Local Dependencies (MRM-LD), and its simplified version, the Multiple Response Model (MRM). These models preserve RC data across MR item types, offering a more comprehensive understanding for MR assessment. Parameters for MRM-LD and MRM were estimated using Markov chain Monte Carlo algorithms in Stan and R. Empirical data from an eighth-grade physics test showed that MRM-LD and MRM outperform Graded Response Model and Nominal Response Model combined with three scoring methods, by retaining more test information, improving reliability and validity, and providing more detailed analysis of item characteristics. Simulation studies confirmed the proposed models perform robustly under various conditions, including small samples and few items, demonstrating their applicability across diverse testing scenarios.

Test fairness is a major concern in psychometric and educational research. A typical approach for ensuring test fairness is through differential item functioning (DIF) analysis. DIF arises when a test item functions differently across subgroups that are typically defined by the respondents’ demographic characteristics. Most of the existing research focuses on the statistical detection of DIF, yet less attention has been given to reducing or eliminating DIF. Simultaneously, the use of computer-based assessments has become increasingly popular. The data obtained from respondents interacting with an item are recorded in computer log files and are referred to as process data. In this article, we propose a novel method within the framework of generalized linear models that leverages process data to reduce and understand DIF. Specifically, we construct a nuisance trait surrogate with the features extracted from process data. With the constructed nuisance trait, we introduce a new scoring rule that incorporates respondents’ behaviors captured through process data on top of the target latent trait. We demonstrate the efficiency of our approach through extensive simulation experiments and an application to 13 Problem Solving in Technology-Rich Environments items from the 2012 Programme for the International Assessment of Adult Competencies assessment.

Belief network analysis (BNA) has enabled major advances in the study of belief systems, capturing Converse’s understanding of the interdependence among multiple beliefs (i.e., constraint) more intuitively than many conventional statistics. However, BNA struggles with representing political divisions that follow a spatial logic, such as the “left–right” or “liberal-conservative” ideological divide. We argue that Response Item Networks (ResINs) have important advantages for modeling political cleavage lines as they organically capture belief systems in a latent ideological space. In addition to retaining many desirable properties inherent to BNA, ResIN can uncover ideological polarization in a visually intuitive, theoretically grounded, and statistically robust fashion. We demonstrate the advantages of ResIN by analyzing ideological polarization with regard to five hot-button issues from 2000 to 2020 using the American National Election Studies (ANES), and by comparing it against an equivalent procedure using BNA. We further introduce system-level and attitude-level polarization measures afforded by ResIN and discuss their potential to enrich the analysis of ideological polarization. Our analysis shows that ResIN allows us to observe much more detailed dynamics of polarization than classic BNA approaches.

Advances in deep learning and representation learning have transformed item factor analysis (IFA) in the item response theory (IRT) literature by enabling more efficient and accurate parameter estimation. Variational autoencoders (VAEs) are widely used to model high-dimensional latent variables in this context, but the limited expressiveness of their inference networks can still hinder performance. We introduce adversarial variational Bayes (AVB) and an importance-weighted extension (IWAVB) as more flexible inference algorithms for IFA. By combining VAEs with generative adversarial networks (GANs), AVB uses an auxiliary discriminator network to frame estimation as a two-player game and removes the restrictive standard normal assumption on the latent variables. Theoretically, AVB and IWAVB can achieve likelihoods that match or exceed those of VAEs and importance-weighted autoencoders (IWAEs). In exploratory analyses of empirical data, IWAVB attained higher likelihoods than IWAE, indicating greater expressiveness. In confirmatory simulations, IWAVB achieved comparable mean-square error in parameter recovery while consistently yielding higher likelihoods, and it clearly outperformed IWAE when the latent distribution was multimodal. These findings suggest that IWAVB can scale IFA to complex, large-scale, and potentially multimodal settings, supporting closer integration of psychometrics with modern multimodal data analysis.

The article proposes a novel item response theory model to handle continuous responses and sparse polytomous responses in psychological and educational measurement. The model extends the traditional two-parameter logistic model by incorporating a precision parameter, which, along with a beta distribution, forms an error component that accounts for the response continuity. Furthermore, transforming ordinal responses to a continuous scale enables the fitting of polytomous item responses while consistently applying three parameters per item for model parsimony. The model’s accuracy, stability, and computational efficiency in parameter estimation were examined. An empirical application demonstrated the model’s effectiveness in representing the characteristics of continuous item responses. Additionally, the model’s applicability to sparse polytomous data was supported by cross-validation results from another empirical dataset, which indicates that the model’s parsimony can enhance model-data fit compared to existing polytomous models.