Hej,
Im working with multilevel (hierarchical) data (Value < level 1 < level 2). When modeling this, using the lmer-function in R, the residuals are by far not normally distributed.
What could be my next steps to analyze this dataset?
Thank you
It is difficult to say if the example use is not known. Because residuals can be used with transformations or use the analysis method "digit-by-digit". Sometimes this helps in difficult cases.
You could try to logarithmize your data. If this doesn't work, you should consider generalized linear mixed models respectively non-linear mixed models. In SAS you could try this using proc genmod or lnmixed.
It's hard to answer your question because the answer depends on the nature of your criterion variable. If it's something like a dichotomous or a count variable, you'd expect that and might solve the problem by employing a link function from the generalized linear model.
What is your DV? Sometime, as suggested by Ann Christina, you can use generalized linear mixed models with an other distribution than normal one. For example, a variable as response time is generally left-skewed. Thus, gamma distribution is more adapted than normal distribution.
It all depends!
At what level is the non-normality - level 1 ,2 etc?
What is the nature of the non-normality - if there are outliers this can make a lot of difference; mild skewness at level 1 would not cause me too much concern.
One solution is to create a rankit variable that is take a normal deviate of the rank of your dependent and then use this as your transformed dependent variable - slope coefficients are then in standard deviational units and can be readily interpreted; and normality assumptions are met This works less well if there are lots of equal ranks.
Finally the normality assumptions apply to the level 1 ,2 etc residuals and not to the raw data.
here is something on rankits
https://en.wikipedia.org/wiki/Rankit
With a large enough sample, your test for normality will always show a deviation. Your skewness and Skurtosis values are mild violations (assuming your software measured excess kurtosis) and thus imho are not an issue here.
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