

Heteroscedasticity at level 1 

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Hello alltogether, I would like to set up a model wehere the level 1 residual variance is explcitly modeled (Snijders & Bosker, 2012, p. 119129), so that the level one random part depends on some covariate (SES = Pupils Socio Economic Status): random_part_at_level_one = R0ij + R1ij * SESij var(R0ij + R1ij * SESij) = sigma0^2 + 2*sigma01*SESij + sigma1^2*SESij How do you achieve this in MPLUS? I would assume that this is done by the model constraint part of the syntax? Could you give me a short example! Thanks! Best regards Linus  Snijders & Bosker (2012). Multilevel Analysis. An Introduction to Basic and Advanced Multilevel Modeling. Los Angeles: SAGE. 


I don't have the S & B book handy right now. Do you want (1) the level1 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 twolevel. 


Hi, I am fitting a multilevel model with a crosslevel interaction, in which a betweenlevel predictor (maternal diagnosis) moderates the random slope coefficient for a withinlevel predictor. I'm interested in understanding how this interaction explains individual differences in my outcome variable. The outcome variable appears to display nonconstant 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 crosslevel 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. 


Modeling with a random slope does to some extent handle heteroscedasticity. 1. With type=twolevel you already get SEs that take clustering into account  and model the heterosc. 2. Might be alright as long as the relationships become (more) linear. 3. Changing estimator doesn't help. 

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