Pre-model Variable Reduction

If anyone knows of better references for this please let me know.

Mark Difford wrote:

Hi All,

I beg to differ with Ravi Varadhan's perspective. While it is true that
principal component analysis does not itself do variable selection, it is
an
important method for pointing the way to what to select. This is what the
methods in the subselect package rely on. (One of its authors was I
believe
a student of Jolliffe's). For a modern perspective on this, see the
following paper:

Debashis Paul, Eric Bair, Trevor Hastie and Robert Tibshirani:
"Preconditioning" for feature selection and regression in
high-dimensional
problems We show that supervised principal components followed by a
variable
selection procedure is an effective approach for variable selection in
very
high dimension. Annals of Statistics 36(4), 2008, 1595-1618.

http://www-stat.stanford.edu/~hastie/Papers/Preconditioning_Annals.pdf

Regards, Mark.

Mark,

Slightly more relevant is the unsupervised sparse principal component 
methods described in the following references.  If anyone knows of 
better references for this please let me know.  -Frank


@Article{zou06spa,
   author = 		 {Zhou, Hui and Hastie, Trevor and Tibshirani, Robert},
   title = 		 {Sparse principal component analysis},
   journal = 	 J Comp Graph Stat,
   year = 		 2006,
   volume =		 15,
   pages =		 {265-286},
   annote =		 {gene microarray;lasso/elastic net;multivariate
analysis;data reduction;singular value
decomposition;thresholding;principal components analysis that shrinks
some loadings to zero}
}
@Article{wit08tes,
   author = 		 {Witten, Daniela M. and Tibshirani, Robert},
   title = 		 {Testing significance of features by lassoed principal 
components},
   journal = 	 Annals Appl Stat,
   year = 		 2008,
   volume = 	 2,
   number = 	 3,
   pages = 	 {986-1012},
   annote = 	 {reduction in false discovery rates over using a vector of 
t-statistics;borrowing strength across genes;``one would not expect a 
single gene to be associated with the outcome, since, in practice, many 
genes work together to effect a particular phenotype.  LPC effectively 
down-weights individual genes that are associated with the outcome but 
that do not share an expression pattern with a larger group of genes, 
and instead favors large groups of genes that appear to be 
differentially-expressed.'';regress principal components on outcome}
}

Ravi Varadhan wrote:

Principal components analysis does "dimensionality reduction" but NOT
"variable reduction".  However, Jolliffe's 2004 book on PCA does discuss
the
problem of selecting a subset of variables, with the goal of
representing
the internal variation of original multivariate vector as well as
possible
(see Section 6.3 of that book).  I do not think that these methods can
handle missing data.  The most important issue is to think about the
goal
of
variable reduction and then choose an appropriate optimality criterion
for
achieving that goal.  In most instances of variable selection, the
criterion
that is optimized is never explicitly considered.

Ravi.

----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage: 
http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Gabor Grothendieck
Sent: Tuesday, December 09, 2008 8:00 AM
To: Harsh
Cc: r-help at r-project.org
Subject: Re: [R] Pre-model Variable Reduction

See:

?prcomp
?princomp

On Tue, Dec 9, 2008 at 5:34 AM, Harsh <singhalblr at gmail.com> wrote:

Hello All,
I am trying to carry out variable reduction. I do not have information 
about the dependent variable, and have only the X variables as it 
were.
In selecting variables I wish to keep, I have considered the following

criteria.

1) Percentage of missing value in each column/variable
2) Variance of each variable, with a cut-off value.

I recently came across Weka and found that there is an RWeka package 
which would allow me to make use of Weka through R.
Weka provides a "Genetic search" variable reduction method, but I 
could not find its R code implementation in the RWeka Pdf file on 
CRAN.

I looked for other R packages that allow me to do variable reduction 
without considering a dependent variable. I came across 'dprep'
package but it does not have a Windows implementation.

Moreover, I have a dataset that contains continuous and categorical 
variables, some categorical variables having 3 levels, 10 levels and 
so on, till a max 50 levels (E.g. States in the USA).

Any suggestions in this regard will be much appreciated.

Thank you

Harsh Singhal
Decision Systems,
Mu Sigma, Inc.

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University