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Significance tests and goodness of fit in the analysis of covariance structures

Significance tests and goodness of fit in the analysis of covariance structures Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models (CSMs). Large-sample theory provides a chi-square goodness-of-fit test for comparing a model (M) against a general alternative M based on correlated variables. It is suggested that this comparison is insufficient for M evaluation. A general null M based on modified independence among variables is proposed as an additional reference point for the statistical and scientific evaluation of CSMs. Use of the null M in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal Ms and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical Ms is also emphasized. Normed and nonnormed fit indices are developed and illustrated. (43 ref) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Psychological Bulletin American Psychological Association

Significance tests and goodness of fit in the analysis of covariance structures

Psychological Bulletin , Volume 88 (3): 19 – Nov 1, 1980

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References (38)

Publisher
American Psychological Association
Copyright
Copyright © 1980 American Psychological Association
ISSN
0033-2909
eISSN
1939-1455
DOI
10.1037/0033-2909.88.3.588
Publisher site
See Article on Publisher Site

Abstract

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models (CSMs). Large-sample theory provides a chi-square goodness-of-fit test for comparing a model (M) against a general alternative M based on correlated variables. It is suggested that this comparison is insufficient for M evaluation. A general null M based on modified independence among variables is proposed as an additional reference point for the statistical and scientific evaluation of CSMs. Use of the null M in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal Ms and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical Ms is also emphasized. Normed and nonnormed fit indices are developed and illustrated. (43 ref)

Journal

Psychological BulletinAmerican Psychological Association

Published: Nov 1, 1980

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