GWR with some parameters held constant

Dear List,
This is more of a conceptual question. Let's say I have a regression model
with a gaussian outcome and two continuous predictors and the model shows
evidence of nonstationarity in one of the beta parameters for the
predictors, but not the other. In this case I may be interested in using GWR
to model the nonstationarity in the first parameter, while holding the
second constant at its OLS estimate. I've used GWR in the past with great
effect, but I think this is an interesting scenario.  I would really like to
hear what everyone thinks about this, and if it would be possible to hack
the gwr() code to make this model possible.

it would be like this:
library(spgwr)
data(columbus)

col.lm <- lm(crime ~ income + housing, data=columbus)
summary(col.lm)
#gives beta (housing) = -0.27

#Let's say that this is assumed stationary, I basically want to keep this
constant in the model, would a quick and dirty way to do this just be:
#this doesn't work of course

col.bw <- gwr.sel(crime ~ income + -(.27*housing), data=columbus,
                 coords=cbind(columbus$x, columbus$y))
col.gauss <- gwr(crime ~ income + -(.27*housing), data=columbus,
                coords=cbind(columbus$x, columbus$y), bandwidth=col.bw)
Either of:

col.lm <- lm(crime ~ housing, data=columbus)
columbus$pred_crime <- predict(col.lm)
col.bw <- gwr.sel(pred_crime ~ income, data=columbus,
   coords=cbind(columbus$x, columbus$y))
col.gauss <- gwr(pred_crime ~ income, data=columbus,
   coords=cbind(columbus$x, columbus$y), bandwidth=col.bw)

col.lm <- lm(crime ~ income + housing, data=columbus)
columbus$h27 <- coef(col.lm)[3]*columbus$housing
col.bw <- gwr.sel(crime ~ income + offset(h27), data=columbus,
   coords=cbind(columbus$x, columbus$y))
col.gauss <- gwr(crime ~ income + offset(h27), data=columbus,
   coords=cbind(columbus$x, columbus$y), bandwidth=col.bw)

do something, the first one includes an intercept twice, the second 
relies on the offset term being handled correctly, which unfortunately it 
isn't. Given the doubts about GWR in Paez et al. 2011, I haven't thought 
it worth the trouble to use more time on the package. I don't think the 
gwrr package offers this variant.

Roger
#And I would want to get the GWR estimates for the location specific effect
of income, while holding the effect of housing constant.

Thanks all for any ideas
Corey Sparks

-----
Corey Sparks
Assistant professor
Department of Demography
The University of Texas at San Antonio
501 West Cesar E Chavez Blvd
San Antonio TX 78207
Corey.sparks 'at' utsa.edu
210 458 3166 &lt;tel:210%20458%203166&gt;
Latitude: 29.423614  /  Longitude: -98.504282
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GWR with some parameters held constant

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