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 Thomas Curran posted on Tuesday, January 26, 2010 - 5:43 pm
I have a very general question, but why do researchers correlate their residual errors in certain structural equation models?

Thanks.

Thom.
 Linda K. Muthen posted on Wednesday, January 27, 2010 - 4:16 pm
I can think of three reasons a model might contain correlated residuals. I'm sure there are many others. In CFA, correlated residuals among the factor indicators might represent a minor factor. In a growth model, auto-correlated residuals might be included. In an SEM model, a residual covariance between two factors might be needed because of an incomplete set of covariates in the regression of the two factors on a set of covariates.
 Jon Elhai posted on Wednesday, January 27, 2010 - 5:23 pm
This might be a relevant paper about correlated residuals:
Cole, D. A., Ciesla, J. A., & Steiger, J. H. (2007). The insidious effects of failing to include design-driven correlated residuals in latent-variable covariance structure analysis. Psychological Methods, 12, 381-398.
 Georg Bruckmaier posted on Monday, March 09, 2015 - 9:35 am
Hi Linda, hi Bengt!

If in a CFA the modindices indicate that a correlation of residuals (of two manifest scales which specify a latent construct) should be allowed in order to substantially improve model fit, this correlation certainly must be justified.

Is it indeed necessary to give a reason why those two (measurement) errors correlate?
How could such a justification look like? Please give me an idea of typical explanations.

Many thanks,
Georg
 Linda K. Muthen posted on Monday, March 09, 2015 - 4:33 pm
You should ask this general question on a general discussion forum like SEMNET.
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