A Bayesian Framework for the Unified Model for Assessing Cognitive Abilities: Blending Theory With Practicality

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Hartz, Sarah McConnell

Contributors dc:contributor

• Stout, William F.

• Psychology, Cognitive

Language dc:language

eng

Identifier

(MiAaPQ)AAI3044108

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87393