I have a dataset that contains data from $307$ subjects and nine variables for each subject. I would like to run a PCA. My problem is that I get a Kaiser-Meyer-Olkin (KMO) value of $0.06$.
Can it be due to the fact that within every subject the variables add up to $1$? Is there another way to test whether it is okay to run PCA on my data?
If the variables sum up to a constant exactly, the correlation or covariance matrix is singular and therefore no Kaiser-Meyer-Olkin (KMO) index can be computed from it. In your case, I suspect, the sum is almost a constant, and KMO was able to compute but it is naturally very low.
PCA can be done with such data as yours. KMO is relevant in the context of Factor analysis, not PCA, though. As for FA, some extraction methods can process singular matrix but others cannot. PCA - you can do it on any numeric data, even it does not make sense at all.
