I have been asked to forward this to the list, any help is appreciated...
Classically we wanted to see how highly some unrelated variable relates to the
locations of my taste stimuli along the x-axis of a 2d-MDS. We call this MDS
a "taste space" since it represents the peceptual similarities among a set of
stimuli.
We find, for example, that a glucose solution has a higher similarity to sucrose
(both "sweet") than e.g. a sodium chloride (salty) solution as reported by 73
subjects. Note, that we calculate the taste similarity by correlating responses
across all subjects to on stimulus with those to another.
Now, for us, the MDS allows us to see all similarities among all taste stimuli
at once.
One question though,is to identify the variables that underlie each axis. For
example, it may well be that those located on one side (e.g. the sweet tasting
stimuli) in general have a higher molecular weight then those on the other side
of an MDS (e.g. bitter tasting ones; along 1 axis).
Hence the regression of stimulus position against e.g. molecular weight.
Now, from the 2d-MDS, as made either by SPSS or Systat, only the total Rsq of
the solution is given, and not separately for each dimension. How to calculate
this? I expected that regressing those distances among all positions would be
onto the similarities of the taste stimuli would yield the Rsq of the MDS solution
in one dimension. This indeed is the case for the 1d-MDS, as long as it's a linear
MDS. The KRuskal MONO method deviates largely from this (I suspect b/c the regressionline
is stepwize; quite misleading IMHO). I don't know about the solution's Rsq along
a single dimension of a 2D-MDS though. And, that's my question.
Regards,
Mark.
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