I´ve got a data set with 82 observations and 220 variables. What I want to do is basically a PCA but with varimax and maybe even oblique rotation of the resulting factors as I want to look for an interpretable result. Afterwards, I want to extract the factor scores.
I tried using prcomp from basic R and principal from the psych package (where I get a bunch of warnings, although it somehow works) . Also, does someone know if a proper parallel analysis is possible with my dataset?
Getting more variables than observations is a problem commonly encountered in chemometrics. Prof. Hermann Wold, a well-known econometrician in Time Series Analysis, has developped a non-linear algorithm based on iterative projections, called NIPALS, that provides a solution to this problem.
You can find it in the R package Chemometrics (P. Filzmoser and K. Varmuza) that offers an implementation of this algoritm, with the nipals function that you can call typing :
> X_nipals
Hi Martin,
There are two main functions in R for PCA (princomp and prcomp). In your case, you can use prcomp because you have more variables than observation.
Example: prcomp(X, scale=TRUE), where X is your data matrix.
Kind regards.
Agreed with Mamoudou;
You can as well use the
package(psych)
and apply the PCA as :
principal(r, nfactors = 1, residuals = FALSE,rotate="varimax",n.obs=NA, covar=FALSE,
scores=TRUE,missing=FALSE,impute="median",oblique.scores=TRUE,method="regression",...)
refer to my attachment - P. 231
Amir
https://www.google.com/url?sa=t&source=web&rct=j&ei=hEK9U-nUHaio4gTvuIGwCA&url=http://cran.r-project.org/web/packages/psych/psych.pdf&cd=2&ved=0CCAQFjAB&usg=AFQjCNGz2ilj_I_XKSAZnYeKkg2VmZcl4g&sig2=t5pOyxelKAIHGKpOoAGR6A
Hi Amir,
thank for the suggestions! You didn´t attach a file so far.
principal seems to be unable to compute factor scores and takes loadings instead, dont know why.
I am sorry, please see the updated answer containing the pdf file of the package "psych" in r.
Getting more variables than observations is a problem commonly encountered in chemometrics. Prof. Hermann Wold, a well-known econometrician in Time Series Analysis, has developped a non-linear algorithm based on iterative projections, called NIPALS, that provides a solution to this problem.
You can find it in the R package Chemometrics (P. Filzmoser and K. Varmuza) that offers an implementation of this algoritm, with the nipals function that you can call typing :
> X_nipals
Another possibility is to bootstrap your analysis in order to asses the "stability" of the results. If they could be considered as "stable", then the sample size does not matter (too much...).
See also: https://www.encorewiki.org/display/~nzhao/The+Minimum+Sample+Size+in+Factor+Analysis
Best,
S.
PLS is your friend. PCA can only deal with n < p.
You may use the R-package pls for it.
Try to extend the dimensionality. Check Ivica Kopriva for references. It is especially good with images, tested in practice. Second question is - why factor analysis? There is a nice collection of algorithms for Matlab written by Andrzej Cichocki.
prcomp() function from stats package is available in R for cases like you mentioned. Hope this helps
I agree with Soutry and Nagdev, respectively: FactoMineR and prcomp solutions can effectively be used for extracting the PCA components when p, the number of variables , is greater than n, the number of observations ("horizontal" files).
These solutions are based on the SVD (Singular Value Decomposition) algorithm (Golub & Reinsch, 1970), a variant of the (Golub & Kahan, 1965) algorithm.
The numerical precision of this algorithm will be as better as p is far greater than n.
However, if your data are centered, you must use only n-1 observations in order to avoid degenerated estimates.
Best regards.
You can still do Principal Components Analysis (which may be thought of as a primitive type of Factor Analysis); it does not assume that the covariance matrix is positive definite, as EFA does.
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