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Re: st: PCA components independent?
There are various issues intertwined here.
1. Uncorrelated does not necessarily mean independent.
For example, a quadratic relation could yield a
zero correlation, depending on marginal distribution,
but it would show dependence nevertheless.
2. Spearman correlation measures strength of monotonic
relationship, not strength of linear relationship.
Many texts have little zoos of scatter plots showing
examples in which Pearson and Spearman give similar
results, and examples in which they do not.
3. In order to understand what is going on
in your data, -scatter f1 f2-.
N.B. -score- is a command, not an option.
After running the PCA command in 9 time series, I use the SCORE option
to extract the first two common components. This is what I do:
. pca s*, fa(2)
. score f1 f2
What puzzles me is the following:
. spearman f1 f2
Number of obs = 61
Spearman's rho = 0.3477
Test of Ho: f1sov and f2sov are independent
Prob > |t| = 0.0060
Where I reject independence. I thought that by construction, they should
be orthogonal. A regular PWCORR command produces the following output:
. pwcorr f1 f2, sig
| f1 f2
f1 | 1.0000
f2 | -0.0000 1.0000
Where correlation is zero but p-value is 1. Any ideas as to why
spearman's test fails to reject independence and I get such p-value in
the regular correlation command?
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