自动确定心理测评中潜在维度数,比传统方法更快更准。
An efficient adaptive dimension selection algorithm for multidimensional probit graded response models

- 用累积收缩先验动态调整潜维数量,冗余维度自动压缩至零。
- 模拟和真实数据均显示能准确恢复潜结构,计算效率高于固定维度法。
- 适合心理与教育评估中需自动识别潜因子的研究者使用。
多维等级反应模型(MGRMs)广泛用于心理与教育测评中的有序问卷数据分析。其核心挑战在于确定潜维数量。传统方法通常拟合多个固定维度模型,并通过AIC、BIC或交叉验证选择最优模型,计算成本高且忽略维度不确定性。本文提出一种基于贝叶斯的自适应维度选择框架,针对概率型MGRMs,利用累积有序尖峰-平滑(COSS)先验对项目载荷矩阵的列方差进行建模,实现潜维间递增收缩,使冗余维度趋近零,同时保留活跃维度灵活性。结合Albert-Chib隐变量扩充处理序次概率似然,得到项目载荷与潜特质的条件高斯更新,与阈值及收缩参数的吉布斯更新协同构成高效自适应采样器。模拟研究评估了该方法在维度恢复、参数估计精度与计算效率方面的表现,对比传统固定维度估计与模型选择流程。结果表明,该方法能准确恢复潜结构,避免重复拟合多个候选维度。进一步在真实心理测评数据上验证,展示其在揭示可解释潜结构上的实用价值。
原文摘要 · Abstract (English)
Multidimensional graded response models (MGRMs) are widely used for analyzing ordinal questionnaire data in psychological and educational assessments. A central challenge in applying these models is determining the number of latent dimensions. Conventional approaches usually fit multiple fixed-dimensional models and select among them using post-hoc criteria such as AIC, BIC, or cross-validation, which can be computationally demanding and ignore uncertainty in dimensionality during estimation. We develop an adaptive Bayesian dimension selection framework for probit MGRMs. Building on the cumulative shrinkage process, we assign a cumulative ordered spike-and-slab (COSS) prior to the column-specific variances of the item loading matrix. This prior induces increasing shrinkage across latent dimensions, allowing redundant dimensions to be shrunk toward zero while preserving flexibility for active dimensions. Albert--Chib latent response augmentation is used to handle the ordinal probit likelihood, yielding conditionally Gaussian updates for item loadings and latent traits. These updates are combined with Gibbs updates for threshold and shrinkage parameters in an efficient adaptive sampler. Simulation studies evaluate the proposed method in terms of dimension recovery, parameter estimation accuracy, and computational efficiency, with comparisons to conventional fixed-dimensional estimation and model selection procedures. The results show that the proposed approach accurately recovers the latent structure while avoiding repeated model fitting over multiple candidate dimensions. We further illustrate the method using real psychological assessment data, demonstrating its practical utility for uncovering interpretable latent structures in ordinal item responses.
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