Dissertation
On the feasibility of applying the No U-Turn Sampler to small-sample item parameter estimation in two-parameter logistic item response theory models
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Spring 2026
DOI: 10.25820/etd.008399
Abstract
Statistical models provide quantitative tools that allow standardized measures of academic ability to be inferred from observed samples of responses to test questions. As a general rule, small sample sizes pose large problems in the computation of measurements that are computationally stable and statistically unbiased. Notably, statistics describing the properties of test questions are particularly susceptible to unstable computation and bias when estimated from small sample sizes. Consequently, modern methods in simulation-based Bayesian inference provide alternatives to mitigate these risks by updating prior beliefs about modeled statistical quantities.
While the inclusion of prior beliefs about calculated estimates aids in facilitating robust estimation, definitions that are too informative or vague still pose significant risks to the feasibility of modern Bayesian algorithms, particularly in operational contexts. Thus, the information quantified in the definitions of prior beliefs may jeopardize the feasibility of modern Bayesian approaches when they are implemented in practice.
The present study examines threats specific to item parameter estimation, focusing on the problems that arise in models of dichotomized (correct versus incorrect item responses) responses. Several replications of tested experimental conditions are performed to evaluate empirical measures of feasibility – including convergence, bias, precision and information observed in simulated item response data – to evaluate the operational feasibility of a frequently used Bayesian algorithm,guided by the evaluation of empirical evidence.
Details
- Title: Subtitle
- On the feasibility of applying the No U-Turn Sampler to small-sample item parameter estimation in two-parameter logistic item response theory models
- Creators
- Nathan DePuy
- Contributors
- Stephen Dunbar (Advisor)Catherine J. Welch (Advisor)Robert Ankenmann (Committee Member)Lia Plakans (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Psychological and Quantitative Foundations
- Date degree season
- Spring 2026
- DOI
- 10.25820/etd.008399
- Publisher
- University of Iowa
- Number of pages
- xiii, 157 pages
- Copyright
- Copyright 2026 Nathan DePuy
- Language
- English
- Date submitted
- 04/23/2026
- Description illustrations
- illustrations, graphs, tables
- Description bibliographic
- Includes bibliographical references (pages 83-92).
- Public Abstract (ETD)
Item response theory models are used to measure question-specific properties in educational assessments. In practice, estimation is difficult when modeling responses from small groups of test-takers. To address the challenges in small-sample estimation, Bayesian item response modeling methods use prior beliefs to inform estimation. While Bayesian methods are generally effective, previous research suggests that the feasibility of small-sample estimation is sensitive to the informativeness of beliefs about the item properties. Using a planned simulation study, the operational feasibility of a popular algorithm called the No U-Turn Sampler is evaluated across experimental conditions that vary according to the informativeness of prior beliefs. Discussion of the reported findings includes practical recommendations, identified limitations, and future research in Bayesian item response modeling.
- Academic Unit
- Psychological and Quantitative Foundations
- Record Identifier
- 9985177272702771
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