Unrestricted within for 2-level CFA?
Message/Author
 Maria Orlando Edelen posted on Wednesday, March 20, 2013 - 12:22 pm
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?
 Linda K. Muthen posted on Wednesday, March 20, 2013 - 1:38 pm
This is possible. On the within level just have an unrestricted model.
 Maria Orlando Edelen posted on Wednesday, March 27, 2013 - 6:21 am
so don't specify anything at all for %within% and specify structure only for %between% in model statement?
 Linda K. Muthen posted on Wednesday, March 27, 2013 - 6:45 am
Yes. Check the results for within to be sure you get the parameters you want. If not, specify those parameters on within.
 Maria Orlando Edelen posted on Wednesday, March 27, 2013 - 8:41 am
I ran it only specifying between structure and the results don't look correct. The fit is terrible, whereas the EFA version was excellent.
 Maria Orlando Edelen posted on Wednesday, March 27, 2013 - 8:45 am
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.
 Maria Orlando Edelen posted on Wednesday, March 27, 2013 - 10:08 am
Linda - I think I'm on my way to solving this. specifying within level covariances among DVs, but I can't specify them all bc model will not be identified.
 Linda K. Muthen posted on Wednesday, March 27, 2013 - 10:53 am
You can specify variances and covariances on the within level. This unrestricted model is identified.
 Maria Orlando Edelen posted on Wednesday, March 27, 2013 - 12:28 pm
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.
 Linda K. Muthen posted on Wednesday, March 27, 2013 - 3:35 pm
I would have a fully unrestricted model on within and ignore the message.
 Sarah Phillips posted on Monday, December 09, 2013 - 9:37 am
Hello,

I wanted to do something similar to Maria (model a 2-level factor structure with an unrestricted model on the within) and want to make sure that I'm using the correct code.

If my model on the between is:
control by m_b113 m_b114 m_b36;

Would my model on the with be:
m_b113 m_b114 m_b36 pwith m_b113 m_b114 m_b36 ?

-Sarah
 Linda K. Muthen posted on Monday, December 09, 2013 - 11:03 am
PWITH pairs the variables on the left-hand side with those on the right-hand side. I don't think that is what you want. Try

m_b113 WITH m_b114 m_b36
m_b114 WITH m_b36;
 Sarah Phillips posted on Monday, December 09, 2013 - 12:06 pm
Thanks, Linda. Just confirming that the code you suggested will give me an unrestricted model on the within?
 Linda K. Muthen posted on Monday, December 09, 2013 - 12:14 pm
If should give you a model of variances and covariances. Check the results to be sure you get what you want.
 Sarah Phillips posted on Monday, December 09, 2013 - 12:21 pm
Thanks!