Dear R experts,

I have a problem that is a related to the question raised in this earlier
post
    https://stat.ethz.ch/pipermail/r-help/2007-January/124064.html

My situation is different in that I have only 2 predictors (coordinates x,y)
for local regression but a number of global ("parametric") offsets that I
need to consider.

Essentially, I have a spatial distortion overlaid over a number of
measurements. These measurements can be grouped by the same underlying value
for each group. The groups are known, but the values are not. We need to
estimate the spatial trend, which we then want to remove. In our
application, the spatial trend is two-dimensional (x,y), and there are about
20 groups of about 50 measurements each. The measurements are randomly
placed. Taking the first group as reference, there are thus 19 unknown
offsets.

The below code for toy data (spatial trend in one dimension x) works for two
or three offset groups, although I have not yet found out how to extract the
fitted values for the globally fit parameters (the offsets).

Unfortunately, the loess call fails for four or more offset groups with the
error message
"Error in simpleLoess(y, x, w, span, degree, parametric, drop.square,
normalize,  :
  only 1-4 predictors are allowed"

Does anyone know of an implementation of local regression with global
(parametric) offset groups that could be applied here, or is there a better
way of dealing with this?

Any comments would be greatly appreciated!

Best regards,
David Kreil.



###
#
# loess with parametric offsets - toy data demo
#

x<-seq(0,9,.1);
x.N<-length(x);

o<-c(0.4,-0.8,1.2#,-0.2  # works for three but not four
     );  # these are the (unknown) offsets
o.N<-length(o);
f<-sapply(seq(o.N),
          function(n){
            ifelse((seq(x.N)<= n   *x.N/(o.N+1) &
                    seq(x.N)> (n-1)*x.N/(o.N+1)),
                    1,0);
          });
f<-f[sample(NROW(f)),];

y<-sin(x)+rnorm(length(x),0,.1)+f%*%o;
s.fs<-sapply(seq(NCOL(f)),function(i){paste('f',i,sep='')});
s<-paste(c('y~x',s.fs),collapse='+');
d<-data.frame(x,y,f)
names(d)<-c('x','y',s.fs);

l<-loess(formula(s),parametric=s.fs,drop.square=s.fs,normalize=F,data=d,
         span=0.4);
yp<-predict(l,newdata=d);

plot(x,y-f%*%o,ylim=c(-3,3));     # spatial distortion
lines(x,yp-f%*%o,pch='+');        # estimate of that
points(x,y,pch='+',col='red');    # input data
points(x,yp,pch='o',col='blue');  # fit of that

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