Hello!
I have a dataset of n=3000 nested within 8 countries with approximately 200 or 400 responses in each country. I originally planned to perform multilevel modelling with 4 dependent variables (DV) as fixed effects in SPSS.
The DV variables are responses in a scale of 1-100 and this kind of variables is treated as metric in psychology.
However, all my DV and the error terms are clearly skewed or clearly curtotic. My questions are:
1. I have read that in some cases the size of the dataset or the number of nesting groups allow to use the general linear model. Does it make sense, however, to do so if the dataset clearly shows extreme tendencies? It looks to me like clearly different distributions, but I am not sure how to define them. Should I regard them as continuous distributions?
2. Am I right to think that data transformation is not a good option if there is a different form of distribution?
3. What would be the advantages and disadvantages of bootstrapping or simulation?
4. What would be good reasons for using a generalized linear or a mixed model?
5. Would it be appropriate to perform a factor analysis of the four DV. If not, are there alternatives?
I would appreciate if someone can answer any of these questions or suggest some not very technical references !
Olga Kostoula If understood your question correctly, you are doing a multivariate analysis since you have four DVs, right? If that is the case, you do not need to worry about the univariate normality. Instead, you should check for the multivariate normality using the Mahalanobis distance, for example. Also, you could visualize that normality using a Q-Q plot. Literature in educational psychology in this matter suggests that if multivariate normality is met, it is safe to assume univariate normality, as well.
Also, have you treated the outlier cases, maybe some multivariate outliers are that cause of the extreme skewness and/or kurtosis. I usually use R's package QuantPsyc to do that using "maria" function.
In the case you conclude that you don't have multivariate normal data, identify which variable is the skewed and follow common data transformation steps, i.e., if it's not severe, so use a square-root transformation; however, if it were more severe, try a log transformation. Also, inverse transformations are only for very strange looking data. Those are heuristics and won't affect your results in any way (Tabachnick & Fidell, 2019).
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