R help - May 2010 - Maximization of quadratic forms

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

> 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
>  
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.