covariance matrix must be positive definite

[Arnoldo Nunes]

I am trynig to use the factoran with matrix 10773x529, but the error
message appears:

The covariance matrix of X must be positive definite.

What it can be happening?
Can somebody help me?

Arnoldo

[Shilpa Gandhi]

I've come across this same problem. Here are my notes from my lab
notebook. Wikipedia says that positive definite describes a
Hermition matrix. "A Hermitian matrix (or self-adjoint matrix) is a
square matrix with complex entries which is equal to its own
conjugate transpose — that is, the element in the ith row and jth
column is equal to the complex conjugate of the element in the jth
row and ith column, for all indices i and j." In other words, my
arrays of covariances or correlations would be Hermitian, bc the
element 2,3 is the same as the element 3,2.

I think part of the answer to this problem is here: <http://www2.gsu.edu/~mkteer/npdmatri.html>


Basically it says you need to take out perfectly correlating
variables and also that large amounts of missing data can lead to a
covariance or correlation matrix not positive definite. I'm still
not sure what pos-def means, but here's an analysis program that
supposedly corrects for data that produces positive-definite
covariance matrices. emcov.exe at <http://www.smallwaters.com/weblinks/>
I haven't made it work yet, so good luck to you.
HTH.

Post by Arnoldo Nunes
I am trynig to use the factoran with matrix 10773x529, but the
error
The covariance matrix of X must be positive definite.
What it can be happening?
Can somebody help me?
Arnoldo

[Peter Perkins]

Post by Arnoldo Nunes
I am trynig to use the factoran with matrix 10773x529, but the error
The covariance matrix of X must be positive definite.
What it can be happening?

Arnoldo, your data matrix is rank-deficient. That is, some of the variables
(columns) are linear combinations of other variables. Can't do factor analysis
with maximum likelihood if that's the case. You need to remove the redundant
variables.

CORRCOEF will give you an indication of pairwise dependence. PRINCOMP might be
of some help. The rank-revealing (i.e. three output form of) QR will give you
one way to remove columns, but there is no unique way to do it, and ultimately
any automated method will probably not do what you want.

Hope this helps.

- Peter Perkins
The MathWorks, Inc.

[stephan]

Does this also happen with closed data (eg. compositional data)?
Therefore a treatment of the data like discussed in Aitchison (The Statistical Analysis of Compositional Data (2003)) or Buccianti et al. (Compositional Data Analysis in the Geosciences (2006)) could be nessesary.

- stephan

[Scott]

Post by Arnoldo Nunes
I am trynig to use the factoran with matrix 10773x529,

but the error

Post by Arnoldo Nunes
The covariance matrix of X must be positive definite.
What it can be happening?
Can somebody help me?
Arnoldo

This is because you are trying to extract more factors
than actually exist in your data.

Scott