Dissertation
Topics in Bayesian generalized latent variable modeling
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Autumn 2024
DOI: 10.25820/etd.007583
Abstract
This dissertation presents two papers in the area of Bayesian generalized latent variable modeling. The first paper introduces a novel Bayesian algorithm for diagnostic classification models, a family of generalized latent variable models that model individuals’ cognitive or psychological states based on their response patterns to a set of observed indicator variables (e.g., surveys, educational assessments, psychological inventories). The proposed algorithm integrates Gibbs sampling – a popular Markov Chain Monte Carlo technique – with Hamiltonian dynamics – a technique that originated in the physics literature for modeling the movement of a particle in a physical system. We show that Gibbs sampling and Hamiltonian dynamics can be combined to create an efficient estimation algorithm for DCMs. The theoretical and computational properties of the algorithm are explored through comprehensive Monte Carlo simulation studies and is applied to a real dataset of clinical patient's responses to a mental health assessment. Results from the simulation studies indicate that the algorithm is capable of providing accurate parameter estimates within a few hundred iterations in well-designed assessments.
The second paper introduces a Beta-Bernoulli mixture item response model (BBM-IRT) for bounded-continuous items such as those often utilized in continuous rating scales and slider-bar assessments. These item types are commonly used in psychological research but, to date, these assessments have primarily been utilized in fixed-length situations, where the same set of items are administered to all respondents, and have not been utilized within an adaptive testing framework. An adaptive testing framework offers several benefits, including the ability to obtain higher quality measurement precision with fewer items as items are targeted and administered based on the respondent's previous responses. In addition to introducing the BBM-IRT model, this work also explores the use of the model within an adaptive testing framework. In particular, the item and test information functions -- a component necessary for building adaptive assessments -- is derived and presented in closed form. Through a series of simulation studies, we provide empirical evidence that it is possible to create adaptive assessments for bounded-continuous item types. An application with real data is also provided showing how the BBM-IRT model can be utilized in practical assessment situations.
Details
- Title: Subtitle
- Topics in Bayesian generalized latent variable modeling
- Creators
- Alfonso J Martinez
- Contributors
- Jonathan Templin (Advisor)Lesa Hoffman (Committee Member)Ariel Aloe (Committee Member)Joyee Ghosh (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Psychological and Quantitative Foundations
- Date degree season
- Autumn 2024
- DOI
- 10.25820/etd.007583
- Publisher
- University of Iowa
- Number of pages
- xiv, 196 pages
- Copyright
- Copyright 2024 Alfonso J Martinez
- Language
- English
- Date submitted
- 11/25/2024
- Description illustrations
- illustrations, tables, graphs
- Description bibliographic
- Includes bibliographical references (pages 140-156).
- Public Abstract (ETD)
- This dissertation consists of two papers that introduce new statistical methodologies for analyzing multivariate data common in the social, behavioral, and psychological sciences. The first paper discusses a novel statistical algorithm that is capable of identifying people’s latent attribute states (e.g., psychological symptoms) more efficiently than currently exist- ing statistical techniques. The second paper tackles the problem of dynamically learning an individual’s proficiency level in real time as they interact with a survey or psychologi- cal/educational assessment consisting of items with a “slider-bar” response structure through the development of a novel psychometric framework for bounded-continuous item types.
- Academic Unit
- Psychological and Quantitative Foundations
- Record Identifier
- 9984774548802771
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