[R] Maximization of quadratic forms
Ravi Varadhan
rvaradhan at jhmi.edu
Wed May 19 04:52:06 CEST 2010
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
>
>
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>
> PLEASE do read the posting guide
> and provide commented, minimal, self-contained, reproducible code.
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