NotesFAQContact Us
Search Tips
Back to results
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ968402
Record Type: Journal
Publication Date: 2012-Jun
Pages: 20
Abstractor: As Provided
ISSN: ISSN-1076-9986
Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models
Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning
Journal of Educational and Behavioral Statistics, v37 n3 p367-386 Jun 2012
The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the concept of degrees of freedom of the model. The authors use a simple example to illustrate the theory and also to provide simulations of residuals in three dimensions. They then explain the rationale behind the formula for the residual-based test statistic. The formula for the statistic is deduced using linear algebra and large-sample theory. Details are provided so that this material can be used in graduate instruction. (Contains 1 table and 6 figures.)
SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A