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Residuals and the residual-based statistic for testing goodness of fit of structural equation models

Foldnes, Njål; Foss, Tron; Olsson, Ulf Henning
Journal article, Peer reviewed
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Foldnes_Foss_Olsson_JEBS_2012.pdf (945.6Kb)
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http://hdl.handle.net/11250/93488
Utgivelsesdato
2012
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Sammendrag
The residuals obtained from tting a structural equation model are

crucial ingredients in obtaining chi-square goodness-of- t statistics for the

model. We 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. We use a simple example to illustrate the theory and also

to provide simulations of residuals in three dimensions. We 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.
Beskrivelse
This is the authors’ final, accepted and refereed manuscript to the article
Utgiver
Sage Publications
Tidsskrift
Journal of Educational and Behavioral Statistics

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