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I have a dataset where students are nested within classes, and classes are nested within schools. I am interested in evaluating the effects of a treatment delivered at the student level. The response variable is on a continuous scale. The residuals with a Linear Mixed Model (with classes and school as random factors) are not normally distributed (they show left skewness). Similarly for the random effects.

If this was a 2 level setting, the lack of normality would not be an issue with a Generalized Estimation Equation (GEE). However, I have classes also nested within schools (i.e., a third level of nesting).

Do you know any reference indicating whether GEEs can also be applied in 3 level settings?

What else may I do asides from data transformations or multi-level Boostrap if GEEs are not applicable?

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In case of a continuous outcome, the GEE is almost equivalent to fitting a mixed model and using the sandwich estimator for the standard errors; for more on this, check this answer.

You have not given us any information on what exactly the problem is with the residuals. You could, for example, consider fitting a mixed model with another distribution for your outcome variable.

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