[R] Uses of isoMDS()

[Ross Clement]

Hi. I'm using the isoMDS() function of the MASS library for
multidimensional scaling. I have two questions that I have not been able
to solve by searching through the archives.

(i) What is the exact stress measure used? The text in the help file
says:

     This chooses a k-dimensional (default k = 2) configuration to
     minimize the stress, the square root of the ratio of the sum of
     squared differences between the input distances and those of the
     configuration to the sum of configuration distances squared.
     However, the input distances are allowed a monotonic
     transformation.

I presume that this is Stress-1 from Kruskal's 1964 paper
"Multidimensional scaling by optimising goodness of fit to nonmetric
hypothesis". (I haven't got a copy of this paper but have Borg and
Groenen's book which references it). However, I'm not 100% sure given
the text description in the help file, and note that isoMDS() quotes
stress as a percentage.

As a preparation for using MDS I wrote some MDS code using iterative
majorisation. While I'm sure that isoMDS() produces much better results,
I would still like to do a like-for-like comparison. If I use a straight
correlation measure between the original and recreated distances, then
isoMDS() is considerably (typically about 0.05) better than my program,
but I'd like to have the proper stress comparison.

(ii) I write most of my code in C. I haven't been able to pin down
exactly what the status of linking C to R is. At present I do the
following:

  if ( experiment == MDS )
  {
    writeDistData( "temp.csv" );
    system( "R --no-save < rEuclidean.R >> /dev/null" );
    reread( "temp.points" );
  }
  else if ( experiment == PCA )
  {
    writeRawData( "temp.csv" );
    system( "R --no-save < rEuclidean.pca.R >> /dev/null" );
    reread( "temp.scores" );
  }

with appropriate R commands in the .R files.

This was easy to write, seems to work fine, and doesn't seem too slow.
But, I'd still like to ask if there is a tidier way of achieving the
same effect.

Thanks in anticipation,

Ross-c