Yigit Hulya Duygu, Culpepper Steven Andrew
University of Illinois Urbana-Champaign, Champaign, Illinois, USA.
Department of Statistics, University of Illinois Urbana-Champaign, Champaign, Illinois, USA.
Br J Math Stat Psychol. 2023 May;76(2):372-401. doi: 10.1111/bmsp.12298. Epub 2023 Jan 5.
Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.
诊断模型通过根据一系列细粒度属性对学生知识概况进行分类，为设计形成性评估提供了一个统计框架。学生学习的背景和生态系统可能在技能掌握中发挥重要作用，因此开发将学生协变量纳入诊断模型的方法很重要。纳入协变量可能使研究人员和从业者能够评估新的干预措施或理解背景知识在属性掌握中的作用。现有研究旨在将协变量纳入验证性诊断模型，也称为受限潜在类别模型。我们提出了在探索性受限潜在类别模型中纳入协变量的新方法，该模型联合推断潜在结构并评估协变量对表现和技能掌握的作用。我们提出了一种新颖的贝叶斯公式，并报告了一种使用吉布斯抽样中的梅特罗波利斯算法的马尔可夫链蒙特卡罗算法，用于近似模型参数后验分布。我们报告了关于我们新方法准确性的蒙特卡罗模拟证据，并展示了一个应用程序的结果，该应用程序研究了学生背景知识在概率数据集掌握中的作用。
