I want to fit a single common factor model to seven different types of measurements of the same thing. However, 6 of the methods I expect to have residual errors that are positively correlated. I expect the intercorrelations to be the same among these 6 methods (fortunately) so I want to build in this assumption. There would be too many correlations to estimate separately. So I want to assume rho is the same and need to constrain, say, cov23 = sigma2sigma3rho, cov24=sigma2sigma4rho, etc. But I don't see how to do this using mxConstraints. If I include all the covariances cov23, cov24 etc. in mxPath statements, and build in the constraints directly, it tells me it doesn't know what rho is. If I code it as shown in the attached file, it estimates a model that is unidentified - every time I run it the parameter estimates change drastically. There is no way as far as I can see to code the mxPath statements so that the covariances equal the standard deviations multiplied by rho.
How can force it to estimate a common correlation rho so that the model is identified?