Heteroscedasticity at level 1
Message/Author
 Linus Trenker posted on Saturday, January 17, 2015 - 6:06 am
Hello alltogether,

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):

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

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Snijders & Bosker (2012). Multilevel Analysis. An Introduction to Basic and Advanced Multilevel Modeling. Los Angeles: SAGE.
 Bengt O. Muthen posted on Tuesday, January 20, 2015 - 11:32 am
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.
 Timothy Allen posted on Tuesday, April 19, 2016 - 8:41 pm
Hi,

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.
 Bengt O. Muthen posted on Friday, April 22, 2016 - 8:52 am
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.