Have 4 dependent and 10 independent variables - which test should I use?


New Member
Hi all,

I'm interested in the potential effects of water pollution on feather color of a bird. For this, I calculated 4 color variables for each individual (brightness, hue, blue chroma and UV chroma), which are my 4 dependent variables. My independent variables (explanatory) are the concentrations of 10 different metals in their blood. I was planning on doing a multiple linear regression for each color variable (e.g. brightness ~ Al + As + Cr + Cd + Ca + Zn and the same for hue, blue chroma and UV chroma), but my data is highly heteroscedastic and there is very high collinearity (calculated with VIF) among my independent variables (as would be expected if some metals come from the same source). Therefore, I was suggested to do a non-parametric test, such as a PERMANOVA or a dbRDA. I've been reading on both methods, but PERMANOVA seems to be more appropriate when comparing differences among groups (factor). On the other hand, dbRDA seems to be better when fitting regression-like models but looks pretty complicated and I'd like to make sure it's the right option before I dive into it.

So my questions are:
1. Is it better to do a multivariate than a univariate analysis in my case?
2. If so, is dbRDA the best multivariate option?
3. If not, should I run one multiple regression per dependent variable and try and fix the heteroscedastic and collinear problems?
4. I also read that a good option for collinear data is Ridge Regression. Could this work?

I use R if that helps with the replies.

Thanks in advance for your time and help!!!