[R] System is computationally singular and scale of covariates

[Moshe Olshansky]

Hi,

What do you mean by outer product?

If you have two vectors, say x and y, of lenght n and you define matrix A by A(i,j) = x(i)*y(j) then your matrix has rank one and it is VERY singular (in exact arithmetics).

Is this is what you mean by outer product?

--- On Sun, 16/8/09, Stephan Lindner <lindners at umich.edu> wrote:

> From: Stephan Lindner <lindners at umich.edu>
> Subject: [R] System is computationally singular and scale of covariates
> To: r-help at stat.math.ethz.ch
> Received: Sunday, 16 August, 2009, 9:15 AM
> Dear all,
> 
> 
> I'm running a self-written numerical optimization routine
> (hazard
> model) which includes computing the inverse of the outer
> product of
> the score. I have been getting the above error message
> ("System is
> computationally singular"), and after some tweaking, I
> realized that
> these variables have some high numbers and the problem
> could be
> circumvented by scaling them down (i.e. dividing them by
> 100 or taking
> log). 
> 
> Since this is obviously not the best procedure, and since I
> have to
> estimate more complex models down the rode, I would like to
> understand
> better the reason which causes this problem. It is not a
> multicollinearity issue (I get the error even when using
> one single
> variable), and I think my code is clean (better be
> paranoid
> though). My sense is that the outer product just becomes
> large, and
> these are hard to invert. Maybe there are restrictions
> concering R in
> the size of the numbers? If that is the case, I think I
> would fare
> better scaling down the outer product rather than the
> variable itself,
> but I first wanted to ask the community to get and
> understanding of
> what could be the problem. 
> 
> 
> Thanks a lot,
> 
> 
> 
>     Stephan Lindner
> 
> 
> 
> 
> 
> 
> 
> 
> -- 
> -----------------------
> Stephan Lindner
> University of Michigan
> 
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