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I have a very general question, but why do researchers correlate their residual errors in certain structural equation models? Thanks. Thom. 


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, autocorrelated 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  11:23 am



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 designdriven correlated residuals in latentvariable covariance structure analysis. Psychological Methods, 12, 381398. 


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 


You should ask this general question on a general discussion forum like SEMNET. 

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