R help - Oct 2007 - Linear regression with constraints on the parameters.

Hi there,


Is there an existing package in R that does simple linear regression
with linear constraints on the parameters? Here is the set up:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
y_i = \sum_{k = 1}^K \beta_k x_k + \epsilon_i

where

\sum_{k = 1}^K c_k \beta_k = c_0, for some known constants \{ c_k \}_{k = 0}^K
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




A proposed solution is to consider the following (with \{ d_k \}_{k 0}^K that
are obvious functions of \{ c_k \}_{k = 0}^K):

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\beta_K = d_0 + \sum_{i=1}^{K-1} d_i \beta_i for known d_i

\implies \beta_K x_K = d_0 x_K + \sum_{i=1}^{K-1} d_i \beta_i x_K

\implies y - d_0 x_K = \beta_0 + \sum_{i=1}^{K-1} \beta_i (x_i + d_i  x_K)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



Is there any existing package that does this? Has anyone used the glmc
package to do this sort of thing? An example will be much appreciated.



Thanks a lot,
gopi.

Hi Gopi,

Simple linear regression minimizes sum of squares of
the residuals. So in your case you can use Quadratic
Programming (see quadprog package) to introduce linear
constraints.

Regards,

Moshe.

--- Gopi Goswami <grgoswami at gmail.com> wrote:
> Hi there,
> 
> 
> Is there an existing package in R that does simple
> linear regression
> with linear constraints on the parameters? Here is
> the set up:
> 
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> y_i = \sum_{k = 1}^K \beta_k x_k + \epsilon_i
> 
> where
> 
> \sum_{k = 1}^K c_k \beta_k = c_0, for some known
> constants \{ c_k \}_{k = 0}^K
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> 
> 
> 
> 
> A proposed solution is to consider the following
> (with \{ d_k \}_{k > 0}^K that are obvious functions of \{ c_k \}_{k
> 0}^K):
> 
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> \beta_K = d_0 + \sum_{i=1}^{K-1} d_i \beta_i for
> known d_i
> 
> \implies \beta_K x_K = d_0 x_K + \sum_{i=1}^{K-1}
> d_i \beta_i x_K
> 
> \implies y - d_0 x_K = \beta_0 + \sum_{i=1}^{K-1}
> \beta_i (x_i + d_i  x_K)
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> 
> 
> 
> Is there any existing package that does this? Has
> anyone used the glmc
> package to do this sort of thing? An example will be
> much appreciated.
> 
> 
> 
> Thanks a lot,
> gopi.
> 
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