发表机构
KLATASDS-MOE; School of Statistics, East China Normal University; Zhiyuan School of Liberal Arts,Beijing Institute of Petrochemical Technology（KLATASDS-MOE; 东华大学统计学院; 北京石油化学工业技术学院人文学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多维概率等级响应模型应用中确定潜在维度数量的挑战，提出自适应贝叶斯维度选择框架，基于累积收缩过程分配先验，结合多种更新形成自适应采样器，经模拟和真实数据验证能准确恢复潜在结构且计算高效。
AI 中文摘要
多维等级响应模型（MGRMs）广泛用于心理和教育评估中的有序问卷数据分析。应用这些模型的一个核心挑战是确定潜在维度的数量。传统方法通常拟合多个固定维度模型并使用诸如AIC、BIC或交叉验证等事后标准进行选择，这可能计算量很大且在估计过程中忽略维度的不确定性。我们为概率MGRMs开发了一种自适应贝叶斯维度选择框架。基于累积收缩过程，我们为项目负荷矩阵的特定列方差分配累积有序尖峰和平板（COSS）先验。该先验会在潜在维度上诱导增加的收缩，使冗余维度向零收缩，同时为活跃维度保留灵活性。使用Albert-Chib潜在响应增强来处理有序概率似然，对项目负荷和潜在特征产生条件高斯更新。这些更新与阈值和收缩参数的吉布斯更新相结合，形成一个高效的自适应采样器。模拟研究在维度恢复、参数估计准确性和计算效率方面评估了该方法，并与传统固定维度估计和模型选择程序进行了比较。结果表明，该方法能够准确恢复潜在结构，同时避免在多个候选维度上重复模型拟合。我们还使用真实的心理评估数据说明了该方法，证明了其在揭示有序项目响应中可解释的潜在结构方面的实际效用。
英文摘要
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.
Comments36 pages, 3 figures, 5 tables
