Multidimensional item response theory (MIRT) provides an important psychometric framework for modeling how multiple latent traits jointly influence observed item responses. In most existing estimation procedures, the latent trait distribution is assumed to be Gaussian. Although computationally convenient, this assumption can be restrictive in many applications where the latent distribution exhibits skewness, heavy tails, or multimodality. More importantly, misspecifying the latent distribution may bias the estimation of item parameters and latent traits. To address this limitation, we propose a data-driven flow-based framework for MIRT models that can capture a broad class of non-Gaussian latent distributions. The proposed approach represents the latent distribution as an invertible transformation of a simple base distribution. For efficient estimation, we further introduce a conditional flow as a function of both the observed response and the noise to approximate the posterior distribution. Under this framework, the item parameters, latent distribution, and posterior approximation can be learned jointly. Comprehensive simulation studies show that the proposed method improves item-parameter and latent-trait recovery when the true latent distribution is non-normal. An application to a personality dataset further illustrates the practical utility of the proposed framework for modeling complex latent trait distributions in large-scale data.

翻译：多维项目反应理论（MIRT）提供了用于建模多个潜在特质如何共同影响观测项目反应的重要心理测量框架。在大多数现有估计流程中，潜在特质分布被假定为高斯分布。尽管计算方便，但在许多应用中，当潜在分布呈现偏态、重尾或多模态时，这一假设可能具有局限性。更重要的是，错误指定潜在分布可能导致项目参数和潜在特质的估计偏差。为解决这一局限，我们提出了一种基于流的、数据驱动的MIRT模型框架，该框架能够捕获广泛的非高斯潜在分布。所提出的方法将潜在分布表示为简单基分布的可逆变换。为实现高效估计，我们进一步引入了一个作为观测反应和噪声函数的条件流来近似后验分布。在该框架下，项目参数、潜在分布以及后验近似可以联合学习。综合模拟研究表明，当真实潜在分布非正态时，所提方法能改善项目参数和潜在特质的恢复。对人格数据集的进一步应用展示了所提框架在大规模数据中建模复杂潜在特质分布的实际效用。