[R] Linear regression with constraints on the parameters.

Moshe Olshansky m_olshansky at yahoo.com
Tue Oct 9 06:00:16 CEST 2007

Hi Gopi,

Simple linear regression minimizes sum of squares of
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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