I would like to set up a model wehere the level 1 residual variance is explcitly modeled (Snijders & Bosker, 2012, p. 119-129), so that the level one random part depends on some covariate (SES = Pupils Socio Economic Status):
I don't have the S & B book handy right now. Do you want (1) the level-1 residual variance to be a function of a covariate, or (2) the random effects to be a function of a covariate? If the former, Mplus doesn't not yet have Constraint=SES implemented for two-level.
I am fitting a multilevel model with a cross-level interaction, in which a between-level predictor (maternal diagnosis) moderates the random slope coefficient for a within-level predictor. I'm interested in understanding how this interaction explains individual differences in my outcome variable. The outcome variable appears to display non-constant error variance. The model is theoretically informed and I can't think of other variables that might account for this distribution in my DV. The N is 196, with 98 families (2 siblings per family).
I have seen three approaches in the literature for handling this problem, and am wondering which you recommend:
1. Using type = complex to compute robust standard errors. I'm uncertain whether this is an option given the cross-level interaction, despite the fact that I'm really only interested in explaining variance across individuals.
2. Transforming the dependent variable (E.g. log transformation).
3. Using a WLS estimator, which I don't believe is available in MPLUS with type = random.