A Bayesian Framework for the Unified Model for Assessing Cognitive Abilities: Blending Theory With Practicality
Hartz, Sarah McConnell
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https://hdl.handle.net/2142/87393
Description
Title
A Bayesian Framework for the Unified Model for Assessing Cognitive Abilities: Blending Theory With Practicality
Author(s)
Hartz, Sarah McConnell
Issue Date
2002
Doctoral Committee Chair(s)
Stout, William F.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Psychology, Cognitive
Language
eng
Abstract
This thesis presents a progression from theory development to real-data application. Chapter 1 gives a literature review of other psychometric models for formative assessment, or cognitive diagnosis models, as an introduction to the Reparameterized Unified Model (RUM), a statistically identifiable, practical cognitive diagnosis model developed by the author from the Unified Model of DiBello, Stout & Roussos (1995). At the end of Chapter 1, a Bayesian framework is given to the model in preparation for the discussion in Chapter 2 of the Markov Chain Monte Carlo algorithm used to estimate the RUM model parameters. Then, the estimation accuracy of the algorithm and the robustness of the estimation is assessed in Chapter 3 with a series of simulation studies. Chapter 4 presents a cognitive diagnosis application of the methodology to data from the preliminary SAT test (PSAT), using the skills-based cognitive structure of the test developed by scientists at the Educational Testing Service. Finally, Chapter 5 gives a cognitive diagnosis of an ACT math test, where the development of skills and the cognitive structure of the test using statistical properties of the test is developed as a more efficient approach to cognitive diagnosis. The progression of this thesis from theory to application provides practitioners with a robust, practical solution to formative assessment.
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