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Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models
Peer reviewed
Direct linkFoldnes, Njal; Foss, Tron; Olsson, Ulf Henning – Journal of Educational and Behavioral Statistics, 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…
Descriptors: Structural Equation Models, Goodness of Fit, Geometric Concepts, Algebra
Smith, Richard M. – 1981
In all latent trait models there is an equation which describes the probabilistic outcome of the interaction of a person with a known ability and an item with a known difficulty. This modeled outcome can be compared to the observed outcome, and the residuals can be summed over the items to assess the fit of the person to the model. Various…
Descriptors: Algebra, Error of Measurement, Goodness of Fit, Guessing (Tests)
