Principal component analysis: low adequacy I am trying to do a Principal Component Analysis to reduce my data from a test battery.
I have a small sample N=58 (It is a selected kind of dog population and due to the Pandemics I am unable to continue my data collection) I originally had 98 variables from my test, I did a pre-data exclusion by let out variables with low variation (<20%) and those highly correlated (taking forward the most relevant of the pair). I finally got 49 variables. However, when I run the PCA in SPSS, the KMO is very low as well as the determinant of the correlations matrix. I already checked the correlation matrix from the PCA for variables not showing correlations >.3 and those highly correlated <.7 (I found 1). Therefore, do you have any advice about how can I take out more variables in an objective, valid way, so I can increase the adequacy of my PCA?
Thanks a lot

I would analyze the covariance matrix of your data to see whether it is different from the random matrix, e.g. you could apply Marchenko-Pastur theorem to the eigen values spectrum. If you determine that all eigenvalues are withim the bounds of the random matrix, then not much can be done with PCA to reduce dimensionality.
