Haberman’s value-added approach is widely used to evaluate the added value of subscores. However, it relies on parameter estimates from sample data and does not account for sampling variability. To address this, Sinharay proposed applying statistical tests to an extended interpretation of the value-added method. Yet, the assumptions underlying these tests may be violated in the context of added value, and a systematic evaluation of their performance has been lacking. This paper examines Sinharay’s approach and introduces two alternatives: applying the tests to the original value-added method and using a non-parametric bootstrap procedure. Simulation results show that the parametric methods fail to adequately control Type I error rates, while the bootstrap procedure offers a more viable alternative.
The growing scale and complexity of statistical and psychometric analyses call for tools that are efficient, flexible, and accessible within the R ecosystem. This article presents R , a high-performance tensor computing framework with automatic differentiation that brings core PyTorch capabilities to R. We offer a hands-on tutorial that demonstrates vectorized computation, automatic differentiation, and Graphics Processing Unit (GPU) acceleration for common tasks, with case studies showing concise code and substantial gains in speed and scalability over base R. Practical guidance for reliable, readable, and reproducible implementation is included. This tutorial emphasizes conceptual clarity and reproducibility, positioning R as a bridge between traditional statistical workflows and modern large-scale computational methods.
Learning increasingly occurs in socially and behaviorally connected environments, yet classical item response theory models treat examinees as independent and estimate latent abilities as free parameters. We introduce a graph neural item response model (GN-IRT) that integrates graph-regularized likelihood with neural representation learning for proficiency estimation in networked settings. GN-IRT preserves the standard two-parameter logistic (2PL) measurement structure while incorporating an observed learner interaction network through a graph-Laplacian penalty and modeling latent abilities as flexible nonlinear functions of learner covariates and network context. Network information regularizes the latent trait without altering the item response function or conditional independence given ability; multilevel and spatial IRT arise as special cases under appropriate adjacency specifications. We analyze the associated penalized latent-trait estimator, establishing existence, uniqueness, asymptotic consistency, preservation of first-order efficiency relative to classical 2PL, and Lipschitz stability under moderate network misspecification. We then show that the neural implementation inherits these first-order properties when approximation and optimization errors are asymptotically negligible. Simulations demonstrate improved ability recovery and predictive performance under joint covariate and network dependence, while preserving classical behavior under independence. An empirical application illustrates interpretable patterns of proficiency alignment in connected learning environments.
Detecting and interpreting differential item functioning (DIF) is critical for ensuring the fairness and validity of measurement instruments. Combinations of psychometric models with data-driven machine learning (ML) approaches have been introduced to facilitate comprehensive DIF analysis across diverse sets of covariates. We review two ML methods for detecting uniform DIF effects (i.e. variation of item difficulty parameters). Rasch trees explore DIF effects with nonparametric decision trees and divide the dataset into subgroups. Regularized moderated Rasch models specify a parametric model for predicting DIF effects. A simulation study illustrates that the optimization strategy and functional form assumptions can result in different conclusions. Finally, we demonstrate the implementation of the methods in practice, using data ( N = 5,193) from the National Educational Panel Study, and provide documented analysis code.
Nonignorable item nonresponses commonly occur in educational and psychological measurement and pose challenges for statistical inference in item response theory (IRT) models. In multidimensional IRT (MIRT), a key issue is identifying the relationships between multiple latent abilities and test items, known as latent variable selection. However, the latent variable selection in MIRT models with nonresponses remains largely unexplored. A common strategy for modeling omissions introduces a latent propensity variable to capture individuals’ tendency to omit items, leading to a joint MIRT model that combines a Rasch model for missingness and a multidimensional two-parameter logistic model for responses. Existing latent variable selection methods are developed mainly for fully observed response data and are not directly applicable when omissions are incorporated through this joint MIRT model. In this article, we develop an efficient expectation model selection (EMS) algorithm for MIRT models with omitted items, termed EMS-OI. Simulation studies show that EMS-OI performs competitively in both latent variable selection and parameter estimation, compared with existing EMS- and expectation maximization-based alternatives. An application to the PISA 2012 dataset further illustrates the proposed EMS-OI algorithm.
