[R-sig-ME] Constraining level 1 error term to 0, Using multivariate multilevel regression modeling

[Jaime Peterson]

Hi R-users,      

We are using a multivariate multilevel regression modeling approach (Goldstein, 1987, 1995) to decompose the total covariance matrix into a within-group and a between-group covariance matrix. Our data comprises of item responses at level 1, students at level 2, and teachers at level 3. We would like to estimate the variance and covariance of the items at the student level and at the teacher level, respectively. For this purpose, the level 1 model is specified as follows: 

Ypig = π_1ig d_1ig + π_2ig d_2ig + . . . + π_pig d_pig

Here,  Ypig is the response on item p, of student i, in teacher group g. The dummy variables (d_1ig to d_pig) represent the P items. The intercept in the equation is dropped. This extra dummy variable level is created only to produce a multivariate response structure, while using software that is designed for univariate analyses.  As a result, there is no level 1 error term in the equation above. However, we have been unable to find R code to constrain the level one (i.e., items) residual variance to be zero. 

Has anyone else encountered this problem? If so, can you please advise as to how you were able to solve it? 

Thank you for any help you can provide,

Best,

-- 
Jaime Peterson
SAESM Co-President
Graduate Teaching Assistant
Department of Educational Psychology
University of Wisconsin-Milwaukee
Ph: 727-504-6934