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Comparison of Three Approaches to Confidence Interval Estimation for Coefficient Omega

Title: A Comparison of Three Approaches to Confidence Interval Estimation for Coefficient Omega.
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Name(s): Xu, Jie, author
Yang, Yanyun, professor directing thesis
Becker, Betsy Jane, 1956-, committee member
Almond, Russell G., committee member
Florida State University, degree granting institution
College of Education, degree granting college
Department of Educational Psychology and Learning Systems, degree granting department
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2014
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource (115 pages)
Language(s): English
Abstract/Description: Coefficient Omega was introduced by McDonald (1978) as a reliability coefficient of composite scores for the congeneric model. Interval estimation (Neyman, 1937) on coefficient Omega provides a range of plausible values which is likely to capture the population reliability of composite scores. The Wald method, likelihood method, and bias-corrected and accelerated bootstrap method are three methods to construct confidence interval for coefficient Omega (e.g., Cheung, 2009b; Kelley & Cheng, 2012; Raykov, 2002, 2004, 2009; Raykov & Marcoulides, 2004; Padilla & Divers, 2013). Very limited number of studies on the evaluation of these three methods can be found in the literature (e.g., Cheung, 2007, 2009a, 2009b; Kelley & Cheng, 2012; Padilla & Divers, 2013). No simulation study has been conducted to evaluate the performance of these three methods for interval construction on coefficient Omega. In the current simulation study, I assessed these three methods by comparing their empirical performance on interval estimation for coefficient Omega. Four factors were included in the simulation design: sample size, number of items, factor loading, and degree of nonnormality. Two thousands datasets were generated in R 2.15.0 (R Core Team, 2012) for each condition. For each generated dataset, three approaches (i.e., the Wald method, likelihood method, and bias-corrected and accelerated bootstrap method) were used to construct 95% confidence interval of coefficient Omega in R 2.15.0. The results showed that when the data were multivariate normally distributed, three methods performed equally well and coverage probabilities were very close to the prespecified .95 confidence level. When the data were multivariate nonnormally distributed, coverage probabilities decreased and interval widths became wider for all three methods as the degree of nonnormality increased. In general, when the data departed from the multivariate normality, the BCa bootstrap method performed better than the other two methods, with relatively higher coverage probabilities, while the Wald and likelihood methods were comparable and yielded narrower interval width than the BCa bootstrap method.
Identifier: FSU_migr_etd-9269 (IID)
Submitted Note: A Thesis submitted to the Department of Educational Psychology and Learning Systems in partial fulfillment of the requirements for the degree of Master of Science.
Degree Awarded: Fall Semester, 2014.
Date of Defense: August 11, 2014.
Keywords: coefficient omega, confidence interval, reliability, structural equation modeling
Bibliography Note: Includes bibliographical references.
Advisory Committee: Yanyun Yang, Professor Directing Thesis; Betsy Becker, Committee Member; Russell Almond, Committee Member.
Subject(s): Statistics
Psychometrics
Quantitative research
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-9269
Owner Institution: FSU

Choose the citation style.
Xu, J. (2014). A Comparison of Three Approaches to Confidence Interval Estimation for Coefficient Omega. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-9269