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

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  • NjÃ¥l Foldnes
  • Tron Foss
  • Ulf Henning Olsson

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.

Suggested Citation

  • NjÃ¥l Foldnes & Tron Foss & Ulf Henning Olsson, 2012. "Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models," Journal of Educational and Behavioral Statistics, , vol. 37(3), pages 367-386, June.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:3:p:367-386
    DOI: 10.3102/1076998611411920
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    References listed on IDEAS

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    1. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
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