SEM variances of residuals fixed to 1? I'm trying to perform structural equations with two second-order latent variables and five first order latent variables (since "a picture is worth a thousand words" I pasted my model below). To perform SEM correctly, I follow steps decribed in a book by Barbara Byrne(2010).
My questions are:


*

*Is it reasonable to fix variances of first order factor
residuals (res_F1--res_F5) to 1?

*Does the choice of reference class (for
setting regression weights to 1) is so crucial? Because, sometimes I
get some results or sometimes AMOS "says" that variance of res_F4 is
negative, which I don't know how to interpret it.



 A: The questions you ask are those of identifying the scale of the latent variables. One possible set of answers is:


*

*No, you keep these error variances freely estimated. The scale of F1 is given by Q; the scale of F2 is given by C; etc. Adding a fixed variance to that will definitely lead to weird results.

*Yes, it is important to choose the variable that is well connected to the underlying factor. To figure out which variable to use as the scale anchor, I would first run the four single-factor models separately fixing the variance of the factors to 1, and look for the variable that has the highest standardized coefficient (or equivalently the highest $R^2$) to use as the anchor in the big model.


Another possible set of answers is:


*

*Yes, you would want to fix these variances to 1, and then also

*You need to free up all of the factor loadings.


That way, your latent variable is scaled by its residual term, and you don't have to agonize over the best measure to use as the scaling factor. 
See also Gonzalez and Griffin 2001, although I think they simply stumbled upon the finite sample sensitivity of Wald tests to reparameterization... a not-terribly-well-known phenomenon even among well-trained statisticians.
Negative values of error variances are spooky indeed. These are sometimes called Heywood cases. Ken Bollen and I have summarized what we knew about them in this paper.
