I am exploring the coordination of plant traits through PCA. The first dimension explains a high proportion of inertia, so I used a broken stick model to help with the decision of how many dimensions to keep.
The theory seems quite straightforward: if the % eigenvalue is above the predicted value from the broken stick model, the dimension should be kept. From what I found on internet, a common result is that you have the first, second, third, n dimensions in that case (let's cal it "A"), and then %eigenvalues for the following dimensions are lower ("B"). So there is a clear distinction between dimensions to keep or not.
With my data, the first, third and fourth dimensions are "A" while the second is "B". Are there good reasons to keep dimension 1 and not the others? Keep 4 dimensions? Keep dimensions 1, 3 and 4 and reject dimension 2 (seems strange)? Thank you!