compare alpha-diversity when the residuals are not normal distributed

Question

[cuicui]

Hi I have a very simple question here. However, even though I searched some literature I couldn't find a way to resolve it.

First, I have tested shannon, simpson and chao1 of my data. However, at the same time, I have some other factors to adjust. I test my data, but it doesn't fit the normal distribution. And the variance of group is not always the same by using Levene test. So I couldn't use multiple way anova.

I tried lm(shannon ~ x1+x2+x3) and test the residuals. The residuals don't fit normality. So I couldn't use lm. I am wondering if someone could give me some suggestions?

Thanks in advance.