Skip to content

Maximization of quadratic forms

2 messages · Russell Shinohara, Ravi Varadhan

#
Dear R Help,

I am trying to fit a nonlinear model for a mean function $\mu(Data_i, 
\beta)$ for a fixed covariance matrix where $\beta$ and $\mu$ are low- 
dimensional. More specifically, for fixed variance-covariance matrices  
$\Sigma_{z=0}$ and $\Sigma_{z=1}$ (according to a binary covariate $Z 
$), I am trying to minimize:

$\sum_{i=1^n} (Y_i-\mu_(Data_i,\beta))' \Sigma_{z=z_i}^{-1} (Y_i- 
\mu_(Data_i,\beta))$

in terms of the parameter $\beta$. Is there a way to do this in R in a  
more stable and efficient fashion than just using a general  
optimization function such as optim? I have tried to use gnls, but I  
was unsuccessful in specifying different values of the covariance  
matrix according to the covariate $Z$.

Thank you very much for your help,
Taki Shinohara



----

Russell Shinohara, MSc
PhD Candidate and NIH Fellow
Department of Biostatistics
Bloomberg School of Public Health
The Johns Hopkins University
615 N. Wolfe St., Suite E3033
Baltimore, MD 21205
tel: (203) 499-8480
http://biostat.jhsph.edu/~rshinoha
#
Hi Taki,

This should be doable with "gnls" by properly specifying the `weights' argument, although I cannot figure out how to do it without spending much time (someone like Doug Bates would know for sure).

But let me ask you:  did you try the straightforward nonlinear optimization (e.g. optim)?  Did you run into any convergence problems?  Did it take way too much time?   

If \mu(\beta) is not a nasty function, you should be able to provide analytic gradient for your objective function.  This would make nonlinear optimization quite efficient.  

Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Russell Shinohara <rshinoha at jhsph.edu>
Date: Tuesday, May 18, 2010 2:38 pm
Subject: [R] Maximization of quadratic forms
To: r-help at r-project.org