# Homogeneity of variance assumption in a multilevel model

I am confused about the homogeneity of variance assumption in a multilevel model.

I'm developing a linear mixed model with a random intercept, slopes, and residual using SAS PROC MIXED. The data are very unbalanced, with a large proportion of clusters having only one observation (and many more having only two or three observations)--thus the variances of many clusters are zero.

I have tried using PROC GLIMMIX with the Level 1 residuals and the HOMOGENEITY option in the COVTEST statement in order to get direct test of this assumption. However, I repeatedly get errors (optimization cannot be completed; the optimization routine cannot improve the function value), and the test is not produced. If I reduce the dataset to clusters having 3+ observations, I do get (significant) a result, so I imagine that this is related to the structure of the data.

I have read that the residual variances can be incorporated into the model explicitly, removing the need for the assumption, but I don't know how to do this. In any case, I'm not 100% sure about the importance of this assumption in the multilevel context and the impact of violation.

Can you provide enlightenment on the theory and help on the practical aspects? Thank you.