[R] Factor Analysis

ripley@stats.ox.ac.uk ripley at stats.ox.ac.uk
Thu Feb 27 19:41:23 CET 2003

On Thu, 27 Feb 2003, Spencer Graves wrote:

> To obtain an nonsingular estimate of an (n x n) covariance or 
> correlation matrix, you need at least (n+1) observations.  However, you 
> can obtain estimates of the largest k singular values or eigenvalues 
> with only (k+1) observations.  The principal components routine must use 
> something like "eigen" or "svd", which does not require a nonsingular 
> covariance matrix.

That's because principal components analysis is defined for simgular 
covariance matrices, but the factor analysis model can never generate 
them.  It's not to do with the computational technique.

Using PCA to find constant combinations is quite common, and such data 
matrices have singular covariance structures.

> rahul.maniar at feri.de wrote:
> > 
> > I am encountering a problem while doing factor analysis in R. I am using
> > correlation matrix of the performance data of funds.And it gives me error
> > message saying singular matrix in use. Now when I try to find the
> > determinant of this matrix it is indeed singular. The problem is when I use
> > same matrix for principal component analysis it works. I was wondering if
> > any of you could help me with this.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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