Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models

Njål Foldnes, Tron Foss and Ulf Henning Olsson

Journal of Educational and Behavioral Statistics, 2012, vol. 37, issue 3, 367-386

Abstract: 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.

Keywords: goodness of fit; residuals; degrees of freedom; residual-based statistic (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:37:y:2012:i:3:p:367-386

DOI: 10.3102/1076998611411920

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