My model consists of a higher-order construct which has two first-order constructs. I am getting good fit in CFA, however on running path analysis, I am not getting such a good fit. Modification indices show that if I correlate error terms between my first-order constructs, I will achieve fit statistics. Can I do that?
With two first-order factors and one second-order factor, it would not make sense to allow the residuals of the first-order factors to correlate. The covariance between the first-order factors is what identifies/is explained by the second-order factor.
Christian Geiser, thanks for your answer, but what if that’s the only way to achieve acceptable fit statistics? Both factors are essentially part of the same construct, so is there any way where correlating their errors can be justified? Will be grateful for your reply.
As far as I understand your model, no, it would not make sense to allow the residuals of the 1st order factors to correlate because their covariance is already accounted for by the 2nd order factor. The misfit could be a sign that your first-order factors are differentially related to your other variables in the path analysis. Have you tried dropping the 2nd order factor and relating your other variables directly to the first-order factors? In that case, correlating their residuals may be reasonable. If you could post a picture (path diagram) of your model as well as other information from the output(s), it would be easier for people to give you advice.
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