# Inflated disturbance estimate

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Joined: 08/26/2012 - 18:16
Inflated disturbance estimate
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I have a complex nonrecursive path model (i.e., only latent disturbance terms for endogenous manifests). It has several reciprocal paths and potential feedback loops. The model converges fine with no errors and the fit statistics all look great (X2 = 9.2, P = 0.24, CFI = 0.99, RMSEA = 0.033) and all the correlation residuals are less than 0.10. However, one of the disturbance estimates is slightly higher than the manifest variables actual variance (d = 1.699, s2 = 1.605), which creates a slightly negative R2 value for that endogenous variable. If I constrain the upper bound of this error to var(manifest x), I get some major changes to the coefficients of other paths.

This was such a subtle problem that I didn't even notice it until I was calculating R2 values for the final publication diagram.

My questions:
1) Would this be considered a Heywood case and thus an inadmissible solution?
2) Does this mean the model is empirically under-identified?

If so, how would you suggest I proceed?

I've attached the script and covariance matrix. Beware, it's huge and ugly but all very justifiable theoretically. I only plan to include paths with p-values < 0.01 in the final diagram.

Thanks, Jeremy

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Joined: 08/26/2012 - 18:16
Inflated disturbance estimate

I just ran across a paper that discusses this exact problem in depth. Apparently, it is common for this to happen when variables touch a reciprocal path, are involved in a feedback loop, or have errors specified to covary. Various methods have been employed to circumvent this issue, but the paper by Hayduk (2006) seems like the most robust solution. I've attached this paper where they illustrate in simple terms how to calculate a more accurate R2 value (i.e., beR2) in these situations.

Cheers, Jeremy

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Joined: 07/31/2009 - 15:12
I'm sorry no one responded to

I'm sorry no one responded to you, but congrats on answering your own question, and thanks for providing the resource!