I have 22 variables with more than 6000 observations. They are highly correlated. I know these data would work as great explanatory variables to a dichotomous event (present absent). Therefore, I intend to combine them via binary logistic regression and, so to avoid multicolinearity, I thought of "orthogonalizing" the original data using PCA. Then I could choose the main modes of variability (or even all the PC's) and use them as the explanatory variables in my regression, once PCs are orthogonal and independent, by definition.
I am running this in MATLAB with function
pca. The variables are nearly normally distributed and are first normalized between 0 +/- 2 standard deviations (around zero because it will be interesting to keep their signal for future analysis, I believe). I also chose not to center the data within the MATLAB function, once they're already normalized.
Now here comes the pitfall. My first 2 PCs (scores) are correlated with r=0.7891! Any hints on this? Any suggestions on mistakes I may be making?
EDIT: In case it lightens th scenario, here is a biplot. Letting PCA center the data, I believe the cloud would be just displaced to around the origin, but still keeping its format / correlation, correct?