R help - Sep 2006 - singular factor analysis

Are there any functions available to do a factor analysis with 
fewer observations than variables?  As long as you have more than 3 
observations, my computations suggest you have enough data to estimate a 
factor analysis covariance matrix, even though the sample covariance 
matrix is singular.  I tried the naive thing and got an error: 

 > set.seed(1)
 > X <- array(rnorm(50), dim=c(5, 10))
 > factanal(X, factors=1)
Error in solve.default(cv) : system is computationally singular: 
reciprocal condition number = 4.8982e-018

      I can write a likelihood for a multivariate normal and solve it, 
but I wondered if there is anything else available that could do this? 

      Thanks,
      Spencer Graves

This is a very common computation in finance.

On the public domain page of the Burns Statistics website
in the financial part is the code and R help file for
'factor.model.stat'.  Most of the complication of the code
is to deal with missing values.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

Spencer Graves wrote:
>      Are there any functions available to do a factor analysis with 
>fewer observations than variables?  As long as you have more than 3 
>observations, my computations suggest you have enough data to estimate a 
>factor analysis covariance matrix, even though the sample covariance 
>matrix is singular.  I tried the naive thing and got an error: 
>
> > set.seed(1)
> > X <- array(rnorm(50), dim=c(5, 10))
> > factanal(X, factors=1)
>Error in solve.default(cv) : system is computationally singular: 
>reciprocal condition number = 4.8982e-018
>
>      I can write a likelihood for a multivariate normal and solve it, 
>but I wondered if there is anything else available that could do this? 
>
>      Thanks,
>      Spencer Graves
>
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