I have a data frame with several different columns of variables (there are categorical predictor variables and several different numeric response variables). I've done a permutational multivariate analysis of variance and then an appropriate post hoc analysis to determine which pairs of groups are actually significantly different.
I want to dig into these results a little more and to determine which of the response variables drive the group differences identified by the analyses. I believe that there should be a way to determine (using vector loadings) which vectors are most aligned with the direction of the significant group differences for each pair of groups that is significantly different.
Although I'm interested in writing an algorithm to find how important each variable is in driving these group differences, my ultimate question is a little more complicated. Is there a statistical analysis I can use that will tell me which variable or variables significantly drive or drives differences between pairs of groups? In other words, if I know that group A and B are significantly different, and that certain variables are aligned more with the direction of this difference (in the direction from group A's centroid to group B's centroid), how can I put p values on each variable to determine if there are any that are especially strongly driving the differences between group A and group B?
Thank you!
