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I have a non-parametric (by which I mean non-normal) data distribution. I tried several transformations, but none were helpful. Now, I want to find a model where I can include random effects with the non-normally distributed data. I know the Kruskal-Wallis test, but I couldn't find any hints if I can include random effects. Does anyone know of an appropriate model?

I do have four different groups with a total N of 328. The dependent variable ranges from 1 to 9. I performed a Shapiro-Wilks tests with this dependent variable for the four groups and all tests were highly significant. I have done some model validation using lme model including the four different groups as a fixed effect and another factor as random effect. The Q-Q plot of this model shows a big bulge at the beginning therefore I assumed that I cannot use the model. The other plots look somehow fine. Please, let me know what else I have to state as I am not really familiar with blogs!

Histograms of the log-transformed dependent variable sorted by the four groups that I want to use as a fixed effect for my model: Histograms of the log-transformed dependent variable sorted by the four groups that I want to use as a fixed effect for my model

This is the model validation of the model I applied.I have used a Linear Mixed-Effects Model with the Groups as fixed effects and an additional random effect.

This is the model validation of the model I applied.

And here is the code I applied

SGroup1 <- lme(Schoollog~Group1, data=T4, random=~1|ID, method='ML')
par(mfrow=c(2,2)) 
plot(fitted(SGroup1),resid(SGroup1)) 
abline(h=0, lty=2) 
qqnorm(resid(SGroup1)) 
qqline(resid(SGroup1)) 
scatter.smooth(fitted(SGroup1), sqrt(abs(resid(SGroup1)))
qqnorm(unlist(ranef(SGroup1))) 
qqline(unlist(ranef(SGroup1))) 
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    $\begingroup$ If you give more information about your data (and research question or hypotheses), someone might point out parametric alternatives (such as a GLMM). That you have non-normal residuals (the distribution of data is not relevant here) doesn't mean that you must use non-parametric methods. $\endgroup$ – Roland May 6 '14 at 15:19
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    $\begingroup$ Please say more about your data. I do not believe that "non-parametric data distribution" actually means anything in statistics. Also note that the data do not have to be normally distributed for a standard model, only the residuals should be, but even those can be somewhat non-normal if you have enough data. Please clarify your situation, your data & your goals more fully. $\endgroup$ – gung - Reinstate Monica May 6 '14 at 15:32
  • $\begingroup$ I do have four different groups with a total N of 328. The dependent variable ranges from 1 to 9. I perforemd a Shapiro-Wilk tests with this dependent variable for the four groups and all tests were highly significant. I have done some model validation using lme model including the four different groups as a fixed effect and another factor as random effect. The Q-Q plot of this model shows a big bulge at the beginning therefore I assumed that I cannont use the model. The other plots look somehow fine. Please, let me know whatelse I have to state as I am not really familiar with blogs! $\endgroup$ – Diana May 6 '14 at 15:41
  • $\begingroup$ Is there a way to upload images? $\endgroup$ – Diana May 6 '14 at 15:45
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    $\begingroup$ Data is data. The adjectives 'parametric' and 'nonparametric' apply to models or methodologies, not to data. Do you simply mean 'not normal' when you say 'nonparametric', or do you intend to imply something more than that? Can you describe your data in more detail? Is it Likert scale, for example? How are you assessing normality? With images, upload them somewhere (say, imgur.com, which stackexchange uses), and give us a link in your post, and someone will fix it for you so we can see your image(s) in your post. $\endgroup$ – Glen_b -Reinstate Monica May 6 '14 at 23:50

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