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

Balamuta, James Joseph

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

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

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

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

Copyright and License Information

Copyright 2021 James Joseph Balamuta

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