Psychometrika最新文献

Social science researchers are generally accustomed to treating ordinal variables as though they are continuous. In this article, we consider how identification constraints in ordinal factor analysis can mimic the treatment of ordinal variables as continuous. We specifically describe model constraints that lead to latent variable predictions equaling the average of ordinal variables. This result leads us to propose minimal identification constraints, which we call integer constraints, that place the latent variables on the scale of the observed, integer-coded ordinal variables. The integer constraints lead to intuitive model parameterizations because researchers are already accustomed to thinking about ordinal variables as though they are continuous. We provide a proof that our proposed integer constraints are indeed minimal identification constraints, as well as illustrations of how integer constraints work with real data. We also provide simulation results indicating that integer constraints are similar to other identification constraints in terms of estimation convergence and admissibility.

Understanding spatial navigation and memory formation is critical to exploring how humans learn and adapt in complex environments. To investigate these processes, we conducted an experiment using the Minecraft Memory and Navigation Task, collecting detailed three-dimensional (3D) path data in a virtual open-world setting. Statistically, we developed a novel methodology to convert complex high-dimensional 3D movement data into functional representations, enabling standardized comparisons and analyses across participants and environments. We applied techniques such as functional clustering and regression to identify navigation patterns and their relationships with cognitive map development and memory retention. Our analysis uncovered two significant insights: first, participants who adopted moderately exploratory behaviors during training demonstrated superior retention of object locations; second, inefficient navigation strategies were strongly linked to poorer spatial memory and navigation performance. These findings highlight the effectiveness of our methodology in advancing the study of navigation behaviors and cognitive processes in dynamic 3D environments.

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.

This work establishes a new identifiability theory for a cornerstone of various cognitive diagnostic models (CDMs) popular in psychometrics: the Q-matrix. The key idea is a novel tensor-unfolding proof strategy. Representing the joint distribution of J categorical responses as a J-way tensor, we strategically unfold the tensor into matrices in multiple ways and use their rank properties to identify the unknown Q-matrix. This approach departs fundamentally from all prior identifiability analyses in CDMs. Our proof is constructive, elucidating a population-level procedure to exactly recover the Q-matrix within a parameter space where each latent attribute is measured by at least two "pure" items that solely measure this attribute. The theory has several desirable features: it can constructively identify both the Q-matrix and the number of latent attributes; it applies to broad classes of linear and nonlinear CDMs with main or all saturated effects of attributes; and it accommodates polytomous responses, extending beyond classical binary response settings. The new identifiability result unifies and strengthens identifiability guarantees across diverse CDMs. It provides rigorous theoretical foundations and indicates a future pathway toward using tensor unfolding for practical Q-matrix estimation.

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.