I am not clear as to how to assess if a multilevel model fit using lmer
satisfies the assumptions of normality and homoscedasticity?
I have used the following r
code and I find that histogram of residuals and qq plot satisfy the assumption that residuals are normally distributed. But as multilevel models have residual both at individual level as well as at the group level, should the residuals at both the levels be normally distributed?
residuals <- resid(results)
summary(residuals)
hist(residuals)
qqnorm(residuals)
qqline(residuals)
xyplot(resid(results) ~ fitted(results))
Best Answer
A multilevel model is defined as $y = Xβ + Zη + ǫ$
Thus there are 3 different kinds of residuals:
Marginal residuals:
Conditional residuals:
Random effects:
In
R
(ifresults
is anmer
object), the commandresiduals(results)
gives you the conditional residuals.The answer is partly copied from the following PowerPoint slide deck pdf.