Hi, I am sorry if this question has been answered somewhere else.
I am wondering about how Mplus deals with binary IVs on level 1 of a multilevel model. When treating these IVs as having both between (level 2) and within (level 1) variance, does the factorization discussed on pages 242-3 of the user's guide (version 6) still apply? How does this address the dependence between the mean and variance of a binary variable?
Or, should binary level-1 IVs be coded as two variables, a cluster mean, specified as between, and the original variable, specified as within? Here I am not clear how specifying the original variable as within would "deal with" its cluster level variation. Can you clarify?
Also, can you please provide a citation that outlines how Mplus deals with this topic.
You are correct. For a binary covariate, you should put it on the WITHIN list for use on within and create a cluster variable for between. You can do this using the CLUSTER_MEAN option of the DEFINE command.