[R] Is there an implementation of loess with more than 3 parametric predictors or a trick to a similar effect? [re-posting as plain text to pass char-set filter]

[Dr. D. P. Kreil (Boku)]

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
undistorted measurement 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, in the most simple scenario. 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.

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"

I tried overriding the restriction and got
"k>d2MAX in ehg136.  Need to recompile with increased dimensions."

How easy would that be to do? I cannot find a definition of d2MAX
anywhere, and it seems this might be hardcoded -- the error is
apparently triggered by line #1359 in loessf.f
      if(k .gt. 15)   call ehg182(105)

Alternatively, 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? I tried lme with
correlation structures but that seems to be much, much slower.

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,pch='+',ylim=c(-3,3),col='red');  # input data
points(x,yp,pch='o',col='blue');           # fit of that

d0<-d; d0$f1<-d0$f2<-d0$f3<-0;
yp0<-predict(l,newdata=d0);
points(x,y-f%*%o);     # spatial distortion
lines(x,yp0,pch='+');  # estimate of that

op<-sapply(seq(NCOL(f)),function(i){(yp-yp0)[!!f[,i]][1]});

cat("Demo offsets:",o,"\n");
cat("Estimated offsets:",format(op,digits=1),"\n");