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
Maximization of quadratic forms
2 messages · Russell Shinohara, Ravi Varadhan
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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