ABSTRACT

Longitudinal item response data are common in social science, educational science, and psychology, among other disciplines. Studying the time-varying relationships between items is crucial for educational assessment or designing marketing strategies from survey questions. Although dynamic network models have been widely developed, we cannot apply them directly to item response data because there are multiple systems of nodes with various types of local interactions among items, resulting in multiplex network structures. We propose a new model to study these temporal interactions among items by embedding the functional parameters within the exponential random graph model framework. Inference on such models is difficult because the likelihood functions contain intractable normalizing constants. Furthermore, the number of functional parameters grows exponentially as the number of items increases. Variable selection for such models is not trivial because standard shrinkage approaches do not consider temporal trends in functional parameters. To overcome these challenges, we develop a novel Bayes approach by combining an auxiliary variable MCMC algorithm and a recently developed functional shrinkage method. We apply our algorithm to survey and review datasets, illustrating that the proposed approach can avoid the evaluation of intractable normalizing constants as well as the detection of significant temporal interactions among items. Through a simulation study under different scenarios, we examine the performance of our algorithm. Our method is, to our knowledge, the first attempt to select functional variables for models with intractable normalizing constants. Supplementary materials for this article are available online.

摘要

纵向项目响应数据在社会科学、教育科学和心理学等学科中很常见。研究项目之间的时变关系对于教育评估或根据调查问题设计营销策略至关重要。尽管动态网络模型已经得到了广泛的发展，但我们不能将它们直接应用于项目响应数据，因为存在多个节点系统，项目之间存在各种类型的局部交互，导致网络结构复杂。我们提出了一个新模型，通过在指数随机图模型框架中嵌入功能参数来研究项目之间的这些时间交互。对此类模型进行推断很困难，因为似然函数包含难以处理的归一化常数。此外，随着项目数量的增加，功能参数的数量呈指数增长。此类模型的变量选择并非易事，因为标准收缩方法不考虑功能参数的时间趋势。为了克服这些挑战，我们通过结合辅助变量 MCMC 算法和最近开发的函数收缩方法来开发一种新颖的贝叶斯方法。我们将我们的算法应用于调查和审查数据集，说明所提出的方法可以避免评估难以处理的归一化常数以及检测项目之间的显着时间交互。通过不同场景下的仿真研究，我们检验了算法的性能。我们的方法是，据我们所知，第一次尝试为具有难以处理的归一化常数的模型选择函数变量。本文的补充材料可在线获取。