I am performing a systematic review of the literature for my dissertation, and I need to extract the relationship between two variables from the results of multivariate analyses, particularly Principal Component Analysis (PCA) and Redundancy Analysis (RDA). In most cases, the article only provides the biplot/triplot and, sometimes, the loadings/correlations. Therefore, those are the only information I have.
I would like to know if I can extract the correlation between two variables only from the biplots. I learned that the angle between the variables reflect their correlation/covariance, i.e., an angle <90º indicates a positive correlation, an angle >90º indicates a negative correlation, and a 90º angle indicates no correlation. However, I have read in some books (e.g., Legendre & Legendre 2012) that only the correlations between variables that are well projected on the PC axes can be inferred using that rule.
So, my questions are 1) Which variables are well projected so I can extract the correlations with confidence? I need to know at least the direction of the correlation with confidence; 2) For poorly projected variables, how can I extract the correlations between them? Is there any solution to this problem?
Thank you
Ref: Legendre, P.; Legendre, L. Numerical Ecology. 3th ed. Elsevier, 2012.
