稀疏贝叶斯多维项目反应理论
Sparse Bayesian Multidimensional Item Response Theory
AI总结：
本文提出一种可扩展的贝叶斯EM算法，用于从混合数据中估计稀疏因子载荷并自动确定潜在因子维度，有效解决了传统MCMC方法在MIRT模型中速度慢且难以实现精确稀疏恢复的问题。
摘要：
多元项目反应理论（MIRT）被寻求在问卷数据的反应模式中寻找可解释（稀疏）解释的应用研究人员广泛需求。然而，在实践中对此类稀疏性发现工具的需求尚未得到满足。我们的论文为二元和有序项目 MIRT 开发了一个贝叶斯平台，该平台需要最少的调整，并且由于其可并行化的特性，在大型数据集上具有良好的可扩展性。MIRT 模型的贝叶斯方法传统上依赖于 MCMC 模拟，这不仅在实际中可能很慢，而且如果不进行额外的阈值处理，通常无法实现精确的稀疏性恢复。在这项工作中，我们开发了一种可扩展的贝叶斯 EM 算法，用于从混合连续、二元和有序项目反应中估计稀疏因子载荷。我们利用贝叶斯非参数工具解决了未知潜在因子维度这一看似不可逾越的问题，该工具能够估计因子的数量。通过参数扩展进行的稀疏旋转进一步增强了收敛性和可解释性，且无需可识别性约束。在我们的模拟研究中，我们表明，即使对于小样本，我们的方法也能在高维合成数据上可靠地恢复因子维度和潜在结构。我们在三个数据集上展示了我们方法的实际有用性：一个教育评估数据集、一个生活质量测量数据集和一个生物行为数据集。所有演示都表明，我们的工具产生了可解释的估计，促进了在纯验证性因子分析设置下可能被忽视的有趣发现。
英文摘要：
Multivariate Item Response Theory (MIRT) is sought-after widely by applied researchers looking for interpretable (sparse) explanations underlying response patterns in questionnaire data. There is, however, an unmet demand for such sparsity discovery tools in practice. Our paper develops a Bayesian platform for binary and ordinal item MIRT which requires minimal tuning and scales well on large datasets due to its parallelizable features. Bayesian methodology for MIRT models has traditionally relied on MCMC simulation, which cannot only be slow in practice, but also often renders exact sparsity recovery impossible without additional thresholding. In this work, we develop a scalable Bayesian EM algorithm to estimate sparse factor loadings from mixed continuous, binary, and ordinal item responses. We address the seemingly insurmountable problem of unknown latent factor dimensionality with tools from Bayesian nonparametrics which enable estimating the number of factors. Rotations to sparsity through parameter expansion further enhance convergence and interpretability without identifiability constraints. In our simulation study, we show that our method reliably recovers both the factor dimensionality as well as the latent structure on high-dimensional synthetic data even for small samples. We demonstrate the practical usefulness of our approach on three datasets: an educational assessment dataset, a quality-of-life measurement dataset, and a bio-behavioral dataset. All demonstrations show that our tool yields interpretable estimates, facilitating interesting discoveries that might otherwise go unnoticed under a pure confirmatory factor analysis setting.
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