University of Illinois Urbana-Champaign

Bayesian estimation of restricted latent class models: Extending priors, link functions, and structural models

Balamuta, James Joseph

Content Files
BALAMUTA-DISSERTATION-2021.pdf

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https://hdl.handle.net/2142/113281

Description

Title
Bayesian estimation of restricted latent class models: Extending priors, link functions, and structural models
Author(s)
Balamuta, James Joseph
Issue Date
2021-07-08
Director of Research (if dissertation) or Advisor (if thesis)
Culpepper, Steven A
Doctoral Committee Chair(s)
Culpepper, Steven A
Committee Member(s)
  • Douglas, Jeffrey A
  • Paquette, Luc
  • Zhang, Susu
Department of Study
Illinois Informatics Institute
Discipline
Informatics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2022-01-12T22:54:58Z
Keyword(s)
restricted latent class models, cognitive diagnosis, latent class, latent structure models, Bayesian, Pólya-gamma data augmentation
Abstract
Restricted latent class models (RLCMs) provide a pivotal framework for supporting diagnostic research that enhances human development and opportunities. In earlier research, the focus was on confirmatory methods that required a pre-specified expert-attribute mapping known as a Q matrix. Recent research directions have led to the creation of exploratory methodology that is able to infer the Q matrix without expert intervention. Within this thesis, we seek to extend and improve upon existing exploratory techniques and applications. We begin by developing novel Bayesian methodology that uses a less restrictive monotonicity condition when estimating the underlying latent structure and attributes. Under the formulation, we make further enhancements by extending the framework to the logit-link function through the Pólya-Gamma distribution. Moreover, we determine different regularization approaches that can be applied to the latent structure to induce sparsity. Next, we propose an extension that seeks to address the dependency structure found among attributes. The dependency structure is able to be described by using a higher-order structure for attributes. Estimating the higher-order structure is done by applying techniques from exploratory factor analysis (EFA). Moreover, the latent structure grows exponentially as the number of attributes increases and we provide an option to specify a subset of the latent structure. Another important consideration is there may be more than one strategy that can be used to achieve success on some tasks. We develop new methods for inferring multiple strategies in the presence of expert knowledge. Lastly, we discuss software implementations of the aforementioned methodological developments. Providing implementations lowers the barrier of entry to employing the methods within psychometric community.
Graduation Semester
2021-08
Type of Resource
Thesis
Permalink
http://hdl.handle.net/2142/113281
Copyright and License Information
Copyright 2021 James Joseph Balamuta

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