论文标题
用于分层潜在结构的多维贝叶斯IRT模型
Multidimensional Bayesian IRT Model for Hierarchical Latent Structures
论文作者
论文摘要
在许多情况下，有理由考虑个人的潜在特征具有层次结构，因此更一般的特征是更具体的特征的合适组成。在建模和/或推理方面，现有的计算这种层次结构特征的项目响应模型具有相当大的限制。在这些局限性和主题的重要性的推动下，本文旨在在建模和推理方面提出一种改进的方法，以在项目响应理论上下文中处理层次结构的潜在特征。从建模的角度来看，所提出的方法允许真正的多维项目和假定的层次结构中的所有潜在特征在相同的尺度上。允许项目是二分或分级响应的。仔细设计了一种有效的MCMC算法，以从所有未知量的模型的关节后分布中进行样本。特别是，所有潜在特征参数均在吉布斯采样算法中的全部条件分布中共同采样。所提出的方法将用于模拟数据和有关巴西敌人考试的真实数据集。
It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such hierarchical structure feature have considerable limitations in terms of modelling and/or inference. Motivated by those limitations and the importance of the theme, this paper aims at proposing an improved methodology in terms of both modelling and inference to deal with hierarchically structured latent traits in an item response theory context. From a modelling perspective, the proposed methodology allows for genuinely multidimensional items and all of the latent traits in the assumed hierarchical structure are on the same scale. Items are allowed to be dichotomous or of graded response. An efficient MCMC algorithm is carefully devised to sample from the joint posterior distribution of all the unknown quantities of the proposed model. In particular, all the latent trait parameters are jointly sampled from their full conditional distribution in a Gibbs sampling algorithm. The proposed methodology is applied to simulated data and a real dataset concerning the Enem exam in Brazil.
