R help - Oct 2010 - how do I make a correlation matrix positive definite?

Hi,

If a matrix is not positive definite, make.positive.definite() function in
corpcor library finds the nearest positive definite matrix by the method
proposed by Higham (1988).

However, when I deal with correlation matrices whose diagonals have to be 1 by
definition, how do I do it? The above-mentioned function seem to mess up the
diagonal entries. [I haven't seen this complication, but obviously all
entries must remain in (-1,1) range after conversion.]

Any R tools to handle this?

I'd appreciate any help.

Hakan Demirtas


	[[alternative HTML version deleted]]

You could use cov2cor() to convert from covariance matrix to
correlation matrix.  If the correlation is >1, the matrix won't be
positive definite, so you can restandardize the matrix to get a pos
def correlation matrix.

Jeremy


On 21 October 2010 15:50, HAKAN DEMIRTAS <demirtas at uic.edu>
wrote:
> Hi,
>
> If a matrix is not positive definite, make.positive.definite() function in
corpcor library finds the nearest positive definite matrix by the method
proposed by Higham (1988).
>
> However, when I deal with correlation matrices whose diagonals have to be 1
by definition, how do I do it? The above-mentioned function seem to mess up the
diagonal entries. [I haven't seen this complication, but obviously all
entries must remain in (-1,1) range after conversion.]
>
> Any R tools to handle this?
>
> I'd appreciate any help.
>
> Hakan Demirtas
>
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>


-- 
Jeremy Miles
Psychology Research Methods Wiki: www.researchmethodsinpsychology.com

On Thu, Oct 21, 2010 at 3:50 PM, HAKAN DEMIRTAS <demirtas at uic.edu>
wrote:
> Hi,
>
> If a matrix is not positive definite, make.positive.definite() function in
corpcor library finds the nearest positive definite matrix by the method
proposed by Higham (1988).
>
> However, when I deal with correlation matrices whose diagonals have to be 1
by definition, how do I do it? The above-mentioned function seem to mess up the
diagonal entries. [I haven't seen this complication, but obviously all
entries must remain in (-1,1) range after conversion.]
>
> Any R tools to handle this?
>
> I'd appreciate any help.
Well, I can't provide immediate help, but I'm curious where the
correlation matrices are coming from. Autocorrelation matrices (i.e.,
cor(x)) are always positive semi-definite (unless you have missing
data and you specify use = "pairwise.complete.observations", in which
case you may get some negative eigenvalues).

The correlation matrix you provided seems to be inconsistent in the
sense that cor (x[, 1], x[, 2]) is -0.95, cor(x[, 2], x[, 3]) is
-0.81, but cor(x[, 1], x[, 3]) is only -0.25. Using basic geometry
arguments one can show that given the 1,2 and 2,3 correlations, the
1,3 correlation must be at least 0.58. Again, you may get such an
apparently inconsistent correlation matrix if you use
"pairwise.complete.observations" and you have enough missing data.

So one question is whether you do use "pairwise.complete.observations"
when you calculate the matrix. If yes, you may want to try specifying
"complete.observations" which will remove more observations but may
solve your problem.

Peter

Hi,

If a matrix is not positive definite, make.positive.definite() function in
corpcor library finds the nearest positive definite matrix by the method
proposed by Higham (1988).

However, when I deal with correlation matrices whose diagonals have to be 1
by definition, how do I do it? The above-mentioned function seem to mess up
the diagonal entries. [I haven't seen this complication, but obviously all
entries must remain in (-1,1) range after conversion.]

Any R tools to handle this?

I'd appreciate any help.


-- 
Beyza Doganay

	[[alternative HTML version deleted]]

I responded to another question that asked the exact same question.  So, I
will repeat my answer here:

Nick Higham (2002) discusses algorithms for this.  One of the algorithms
discussed in the paper is implemented in the "Matrix" package as
`nearPD'
function.

library(Matrix)
?nearPD

Ravi.


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of HAKAN DEMIRTAS
Sent: Thursday, October 21, 2010 6:50 PM
To: r-help at r-project.org
Subject: [R] how do I make a correlation matrix positive definite?

Hi,

If a matrix is not positive definite, make.positive.definite() function in
corpcor library finds the nearest positive definite matrix by the method
proposed by Higham (1988).

However, when I deal with correlation matrices whose diagonals have to be 1
by definition, how do I do it? The above-mentioned function seem to mess up
the diagonal entries. [I haven't seen this complication, but obviously all
entries must remain in (-1,1) range after conversion.] 

Any R tools to handle this?

I'd appreciate any help.

Hakan Demirtas


	[[alternative HTML version deleted]]

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.