Psychometrika最新文献

In psychometric sciences, such as social or behavioral sciences, and, similarly, in medical sciences, it is increasingly common to deal with longitudinal data organized as high-dimensional multidimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often implies a smooth functional structure on one of the tensor modes. To help researchers investigate such data, we introduce a new tensor decomposition approach based on the PARAFAC decomposition. Our approach allows researchers to represent a high-dimensional functional tensor as a low-dimensional set of functions and feature matrices. Furthermore, to capture the underlying randomness of the statistical setting more efficiently, we introduce a probabilistic latent model in the decomposition. A covariance-based block-relaxation algorithm is derived to obtain estimates of model parameters. Thanks to the covariance formulation of the solving procedure and thanks to the probabilistic modeling, the method can be used in sparse and irregular sampling schemes, making it applicable in numerous settings. Our approach is applied in the psychometric setting to help characterize multiple neurocognitive scores observed over time in the Alzheimer's Disease Neuroimaging Initiative study. Finally, intensive simulations show a notable advantage of our method in reconstructing tensors.

Over the past two decades, there has been growing interest in analyzing the effects of educational programs on outcomes using process data from computer-based testing and learning environments. However, most analyses focus on final outcomes at the end of a test or session, overlooking their functional nature over time and neglecting causal mechanisms. To address this gap, this article proposes a novel causal mediation framework for identifying and estimating functional natural direct effects, functional natural indirect effects, and functional total effects, along with their subgroup effects. We define these effects using potential outcomes and provide nonparametric identification strategies depending on whether post-treatment covariates are present or not. We then develop estimation methods using generalized additive models, a flexible and robust tool for analyzing functional data. Through a simulation study, we assess the finite-sample performance of the proposed approach by comparing it to parametric regression methods. We also demonstrate our approach by examining the effects of extended time accommodations on two functional outcomes using process data from the National Assessment of Educational Progress. Our mediation approach with functional outcomes effectively captures dynamic causal mechanisms underlying the program's effects and pinpoints when and for whom each effect manifests throughout the testing period.

Various item selection algorithms have been proposed for cognitive diagnostic computerized adaptive testing (CD-CAT), with the goal of efficiently diagnosing examinees' strengths and weaknesses. However, these algorithms often come with significant computational costs, which can hinder their practical implementation. A likelihood-based profile shrinkage (LBPS) algorithm is proposed to simplify the item selection process and reduce the computational cost in CD-CAT. Our simulation results indicate that incorporating LBPS into existing item selection methods yields substantial computational efficiency gains, with greater reductions in computation time as the number of attributes and test length increase. Additionally, LBPS maintains estimation accuracy at both the attribute and pattern levels. These findings suggest that LBPS is a scalable and effective solution for the item selection of CD-CAT in complex scenarios.

Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the observed covariance matrix. The factor loading matrix captures the linear effects of the factors and, if unrestricted, can only be identified up to an orthogonal transformation of the factors. However, in many applications, the factor loadings exhibit an interesting sparsity pattern that may lead to identifiability up to column signs. We study this phenomenon by connecting sparse confirmatory factor analysis models to bipartite graphs and providing sufficient graphical conditions for identifiability of the factor loading matrix up to column signs. In contrast to previous work, our main contribution, the matching criterion, exploits sparsity by operating locally on the graph structure, thereby improving existing conditions. Our criterion is efficiently decidable in time that is polynomial in the size of the graph, when restricting the search steps to sets of bounded size.

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.