testing linear combinations of coefficients after spatial regression

I'm interested in testing linear combinations of coefficients after models
like spautolm, errorsarlm, and lagsarlm in the spdep package. I'm used to
using "anova" for this, but the anova.sarlm implementation doesn't seem to
permit it straightforwardly. For instance, if I wanted to testing something
like b_1-.25*b_2=0, how would I go about doing that?

See the linearHypothesis() methods in the car package. I think that, after 
someone has checked that all is as it should be, sarlm objects could get a 
vcov() method, which they do not have now. These work formally, but are 
not checked:

library(car)
library(spdep)
example(columbus)
lmobj <- lm(CRIME ~ HOVAL+INC, data=columbus)
linearHypothesis(lmobj, "HOVAL-INC=0", test="Chisq")
lagobj <- lagsarlm(CRIME ~ HOVAL+INC, data=columbus,
   listw=nb2listw(col.gal.nb))
linearHypothesis(lagobj, "HOVAL-INC=0", test="Chisq",
   vcov.=lagobj$resvar[2:5,2:5])
errobj <- errorsarlm(CRIME ~ HOVAL+INC, data=columbus,
   listw=nb2listw(col.gal.nb))
linearHypothesis(errobj, "HOVAL-INC=0", test="Chisq",
   vcov.=errobj$resvar[2:5,2:5])

Please do check that this is an appropriate use of the returned values 
when fitted using eigenvalues. Other steps would be needed when a (mixed) 
numerical Hessian is used to approximate the variance/covariance matrix of 
the coefficients. Then a vcov() method could be added for sarlm objects, 
but it needs caution and analysis.

Hope this helps,

Roger

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Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no

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