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ERIC Number: EJ933084
Record Type: Journal
Publication Date: 2011
Pages: 24
Abstractor: As Provided
Reference Count: 52
ISSN: ISSN-1070-5511
Comparing the Fit of Item Response Theory and Factor Analysis Models
Maydeu-Olivares, Alberto; Cai, Li; Hernandez, Adolfo
Structural Equation Modeling: A Multidisciplinary Journal, v18 n3 p333-356 2011
Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be compared. When applied to a binary data set, our experience suggests that IRT and FA models yield similar fits. However, when the data are polytomous ordinal, IRT models yield a better fit because they involve a higher number of parameters. But when fit is assessed using the root mean square error of approximation (RMSEA), similar fits are obtained again. We explain why. These test statistics have little power to distinguish between FA and IRT models; they are unable to detect that linear FA is misspecified when applied to ordinal data generated under an IRT model. (Contains 2 figures, 4 tables and 5 footnotes.)
Psychology Press. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A