Hello Ahmet,

I presume that what is being suggested is that you link two or more of the error terms/"disturbances" in the manifest variables with a covariance. That is tantamount to asserting that the two manifest/observed variables share some of their specific and/or error variance (the latter condition is a bit more troublesome, as error variance is typically thought of as being independent of other sources in the model).

To the extent that you can muster a justification for these linkages, and the linkages are among variables influenced by the same factor, you'll probably be OK in choosing to add them, with appropriate qualifications, of course. The danger, as you rightly note, is that of overfitting the model, and the resultant, modified model may not generalize well.

However, in the absence of strong justification and/or allowing covariance links among error terms for variable pairs from different factors, many folks would rightly be concerned as to the legitimacy of those added links.

Finally, note that multiple covariance links among variables associated with a given factor might be suggestive that the basic factor model is incorrect; perhaps a second-order, a bi-factor, or some other model would be better suited.

Good luck with your work.

I agree with you that error/residual covariances require theoretical explanation/justification, especially when they are added post hoc based on model modification indices or an inspection of the model residual covariance matrix. Reasons for shared residual variance can be similar item wording, shared method variance, or the existence of additional factors.

One problem with residual covariances is that they lead to an underestimation of the model-estimated indicator reliabilities and confounding of random error variance with systematic item-specific variance. In cases where there's a clear theoretical and/or substantive explanation for the presence of shared residual variance, adding additional factors (e.g., method factors) or splitting up a single factor into two correlated factors is often a better choice from a psychometric perspective.

Hi:

Freeing error covariance between items from a single factor would be ok, though this should be explained theoretically in the Discussion part. I suggest you see page 9th of the following article: INTEGRATING ALTERNATIVE CONCEPTIONS OF PSYCHOPATHIC PERSONALITY: A LATENT VARIABLE MODEL OF TRIARCHIC PSYCHOPATHY CONSTRUCTS.