R help - Dec 2004 - System is computationally singular?

Hi all,

I was using the Newton-Raphson method to estimate paremeters in the model
developed by my supervisor. However, when I interatively computed
theta(t+1)=theta(t) - solve(H)*s (where the Hessian matrix and score vector were
explicitely derived), I got the error message: Error in solve.default(H) :
system is computationally singular: reciprocal condition number = 1.70568e-032.
Assume my score vector and Hessian matrix were correct, could anyone give me
some suggestion on how to avoid this singular situation? Thank you in advance.
Maybe this question is not related to R itself, but it is kind of statistical
computation problems, please forgive me to put questions here.

Rui

Hi Rui,

when you are far from the optimum the Hessian might be a non positive 
definite matrix and thus it cannot be solved. There are some positive 
definite modifications that you could apply. For more info you could 
check at Section 3.2.4 of:

http://www.stat.wisc.edu/~mchung/teaching/stat471/stat_computing.pdf

However, if you have a function computing the minus log-likelihood and 
its derivative, then it would be easier to use `optim()', probably 
with method "BFGS" (or "CG" if you have many parameters).

I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat
     http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm


----- Original Message ----- 
From: "Rui Wang" <wangruiwin at hotmail.com>
To: <r-help at stat.math.ethz.ch>
Sent: Thursday, December 09, 2004 4:16 AM
Subject: [R] System is computationally singular?

> Hi all,
>
> I was using the Newton-Raphson method to estimate paremeters in the 
> model developed by my supervisor. However, when I interatively 
> computed theta(t+1)=theta(t) - solve(H)*s (where the Hessian matrix 
> and score vector were explicitely derived), I got the error message: 
> Error in solve.default(H) : system is computationally singular: 
> reciprocal condition number = 1.70568e-032. Assume my score vector 
> and Hessian matrix were correct, could anyone give me some 
> suggestion on how to avoid this singular situation? Thank you in 
> advance. Maybe this question is not related to R itself, but it is 
> kind of statistical computation problems, please forgive me to put 
> questions here.
>
> Rui
>
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