Simon, thank you very much for your very instructive response!
Your explanation has not only justified my intuitive solution to just delete the corresponding row & column of the penalty matrix, when choosing a reference category for dummy coding, but leads to a much better understanding of this important issue. Thanks again, Daniel Simon Wood schrieb: > Daniel, > > There's nothing built in to constraint the coefficients in this way, but it's > not too difficult to reparameterize to impose any linear constraint. The key > is to find an orthogonal basis for null space of the constraint. Then it's > easy to re-parameterize to work in that space. Here's a simple linear model > based example .... > > ## simulated problem: linear model subject to constraint > ## i.e y = X b + e subject to C b=0 > X <- matrix(runif(40),10,4) ## a model matrix > y <- rnorm(10) ## a response > C <- matrix(1,1,4) ## a constraint matrix so C b = 0 > > ## Get a basis for null space of constraint... > qrc <- qr(t(C)) > Z <- qr.Q(qrc,complete=TRUE)[,(nrow(C)+1):ncol(C)] > > ## absorb constraint into basis... > XZ <- X%*%Z > > ## fit model.... > b <- lm(y~XZ-1) > > ## back to original parameterization > beta <- Z%*%coef(b) > sum(beta) ## it works! > > ## If there had been a penalty matrix, S, as well, > ## then it should have been transformed as follows.... > > S <- t(Z)%*%S%*%Z > > ... So provided that you have the model matrix for the term that you want to > penalize in `gam' then it's just a matter of transforming that model matrix > and corresponding penalty/ies, using a null space matrix like Z. > > Note that the explicit formation of Z is not optimally efficient here, but > this won't have a noticeable impact on the total computational cost in this > context anyway (given that mgcv is not able to make use of all that lovely > sparcity in the MRF, :-( ). > > Hope this helps. > > best, > Simon > > > > > On Saturday 07 February 2009 21:00, Daniel Sabanés Bové wrote: > >> Dear Mr. Simon Wood, dear list members, >> >> I am trying to fit a similar model with gam from mgcv compared to what I >> did with BayesX, and have discovered the relatively new possibility of >> incorporating user-defined matrices for quadratic penalties on >> parametric terms using the "paraPen" argument. This was really a very >> good idea! >> >> However, I would like to constraint the coefficients belonging to one >> penalty matrix to sum to zero. So I would like to have the same >> centering constraint on user-defined penalized coefficient groups like >> it is implemented for the spline smoothing terms. The reason is that I >> have actually a factor coding different regions, and the penalty matrix >> results from the neighborhood structure in a Gaussian Markov Random >> Field (GMRF). So I can't choose one region as the reference category, >> because then the structure in the other regions would not contain the >> same information as before... >> >> Is there a way to constraint a group of coefficients to sum to zero? >> >> Thanks in advance, >> Daniel Sabanes >> > > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
