[R] Bootstrapped eigenvector

[Jérôme Lemaître]

Hello alls,

I found in the literature a technique that has been evaluated as one of the
more robust to assess statistically the significance of the loadings in a
PCA: bootstrapping the eigenvector (Jackson, Ecology 1993, 74: 2204-2214;
Peres-Neto and al. 2003. Ecology 84:2347-2363). However, I'm not able to
transform by myself the following steps into a R program, yet?

Can someone could help me with this?

I thank you very much by advance.

Here are the steps that I need to perform:
1) Resample 1000 times with replacement entire raws from the original data
sets (7 variables, 126 raws)
2) Conduct a PCA on each bootstrapped sample
3) To prevent axis reflexion and/or axis reordering in the bootstrap, here
are two more steps for each bootstrapped sample
3a) calculate correlation matrix between the PCA scores of the original and
those of the bootstrapped sample
3b) Examine whether the highest absolute correlation is between the
corresponding axis for the original and bootstrapped samples. When it is not
the case, reorder the eigenvectors. This means that if the highest
correlation is between the first original axis and the second bootstrapped
axis, the loadings for the second bootstrapped axis and use to estimate the
confidence interval for the original first PC axis.
4) Determine the p value for each loading. Obtained as follow: number of
loadings >=0 for loadings that were positive in the original matrix divided
by the number of boostrap samples (1000) and/or number of loadings =<0 for
loadings that were negative in the original matrix divided by the number of
boostrap samples (1000).



Thanks again

Jérôme Lemaître

Étudiant au doctorat
Chaire Industrielle Sylvicuture-Faune, Forêt Boréale, Côte-Nord
& Département de biologie,
Faculté des sciences et de génie
Pavillon Alexandre-Vachon
Université Laval
Québec, QC  G1K 7P4
tél : (418) 656-2131 poste 2917
Local : VCH-2044
Courriel: jerome.lemaitre.1 at ulaval.ca