I've run an EFA for a two-level model and am interested in further developing the solution using CFA that specifies the structure at the between level but uses an unrestricted solution for the within level. As I understand it, this is sort of opposite from using the cluster statement to handle the between and specifying the within. In my case, the covariance of interest is between (teachers) and the 'noise' is within (ratings, classes, segments). Is there a way to do this in CFA?
I don't understand how to specify an unrestricted model. Isn't the whole point of unrestricted that you don't have to specify it? The EFA output does not provide the parameter estimates from an unrestricted within so there is nothing to try to replicate for CFA. The CFA that I ran, specifying nothing on the within only produced the variances for within, so I don't think it is modeling any structure there at all.
I tried to specifically estimate all within level variances and covariances in addition to the 2-factor structure at the between level and got a warning that the model may not be identified and I needed to have fewer parameters than # of clusters. so i reduced the number of modeled within level covariances. The end result when I finally got the # of parameters below the # of clusters seems reasonable.