Some advances in Bayesian variable selection, cognitive diagnostic modeling, and process data analysis

Chapter 1: Selecting subsets of variables has always been a vital and challenging topic in educational and psychological settings. In many cases, the probability that an interaction is active is influenced by whether the related variables are active. In this study, we propose a hierarchical prior for Bayesian variable selection to account for a structural relationship between variables and their interactions. Specifically, an interaction is more likely to be active when all the associated variables are active and is more likely to be inactive when at least one variable is inactive. The proposed hierarchical prior is based upon the deterministic inputs, noisy “and” gate model and is implemented in the stochastic search variable selection approach (George & McCulloch, 1993). Metropolis-within-Gibbs algorithm is used to uncover the selected variables and estimate the coefficients. Simulation studies were conducted under different conditions and in a real data example. Performance of the proposed hierarchical prior was compared with those of the widely used Bayesian variable selection approaches with standard independent prior, including traditional stochastic search variable selection prior, Dirac spike and slab priors (Mitchell & Beauchamp, 1988), and hyper g-prior (Liang et al., 2008). Chapter 2: The development of online learning systems exposes students to more learning resources and makes it possible to utilize effective instructional materials. While learning systems have been improved from various perspectives, applying instructional interventions with change point detection approaches has not been investigated. This study proposes a framework that applies instructional interventions for learning acceleration and detection. Firstly, we propose a longitudinal cognitive diagnostic model with instructional intervention covariates. The interventions’ parameters are estimated via a Gibbs sampling algorithm based on historic response data. We then implement the estimated parameters in a change acceleration and detection approach for the learning process, demonstrating that the model could be used to increase the learning rate. Simulation studies are conducted to examine parameter recovery, learning efficiency, and detection accuracy of the proposed framework. Chapter 3: Complex problem-solving skill has been recognized as one of the key competencies and their measurement has drawn an increasing interest in recent years. Computer-based simulated interactive tasks serve as a popular tool for measuring problem-solving skill. Through students’ process of finishing the tasks, students’ actions and the corresponding timestamps can be recorded, which provides detailed information for further insights into students’ problem-solving skills. In this study, we distinguish the process of information retrieval and information integration and application during the problem-solving process. Based on this conceptualization, we propose a joint modeling framework for responses, response times, and information retrieval. Model parameters were estimated using the Gibbs sampling approach. A real data from Program for International Student Assessment 2012 was analyzed. The estimated parameters from real data application were utilized in a follow-up simulation study, which examines the parameter recovery of the proposed joint model.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Psychology

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Li, Anqi

Contributors dc:contributor

• Culpepper, Steven A
• Zhang, Susu
• Chang, Hua-Hua
• Douglas, Jeffrey A
• Koehn, Hans Friedrich

• Bayesian Variable Selection
• Strong Heredity
• Stochastic Search Variable Selection
• Cognitive Diagnostic Model
• Learning Intervention
• Change Acceleration
• Change Detection
• Process Data
• Information Retrieval
• Complex Problem Solving
• Joint Model

Statement dc:rights

• Copyright 2024 Anqi Li

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/125821

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F125821