Abstract

In this paper, we propose a multilevel multidimensional item response model for studying the relations among multiple abilities and covariates in a hierarchical data structure. As an example, this study is well suited to examining the scenario in which a test measures multidimensional latent traits (e.g., reading ability, cognitive ability, and computing ability) and in which students are nested within classes or schools. The new model can recover the correlations among multidimensional abilities, along with the correlation between person- and school-level covariates and abilities. A fully Gibbs sampling algorithm within the Markov chain Monte Carlo (MCMC) framework is proposed for parameter estimation. A unique form of the deviance information criterion (DIC) is used as a model comparison index. Two simulation studies show that the estimation method is suitable in recovering all model parameters.

摘要

在本文中，我们提出了一种多级多维项目响应模型，用于研究分层数据结构中多种能力和协变量之间的关系。例如，本研究非常适合检查测试测量多维潜在特征（例如阅读能力、认知能力和计算能力）以及学生嵌套在班级或学校中的场景。新模型可以恢复多维能力之间的相关性，以及个人和学校层面的协变量与能力之间的相关性。提出了马尔可夫链蒙特卡罗（MCMC）框架内的完全吉布斯采样算法用于参数估计。使用偏差信息准则（DIC）的独特形式作为模型比较指标。