> -----Original Message-----
> > I would like to calculate the RELATIVE euclidean distance.
> Is there a
> > function in R which does it ?
> >
>
> A simple solution to this is to transform the data and then
> compute the Euclidean distance using dist().
>
> decostand(foo, method = "normalize") and
>
> disttransform(foo, method = "chord") in package BiodiversityR
>
See also ?scale in the base package, which will centre and scale by sd by
default.
But 'relative euclidean distance' is not that straightforward to explain.
'Relative' usually means 'divided by the true (or mean) value', or at least it
does for most chemists. You almost certainly don't mean 'euclidean distance
divided by mean euclidean distance'. I suspect - because I'm a chemist and it's
what I'd by considering in your shoes - that what you're asking for is the
euclidean distance between points defined by concentrations of your 94 analytes
scaled by mean value.
scale() will (by default) scale by dividing by centring on means and dividing
by the sd, and that is usually the most sensible thing to do for multivariate
data sets where the units or scales for each variable are very different.
Scaling by sd and scaling by mean value could give appreciably different
answers. Although relative sd for chemical measurement is often near-constant
over modest ranges, there is no particular reason to expect that the sd is
strictly proportional to the mean over orders of magnitude, and in fact it
generally isn't (relative SD tends to be larger for low-level analytes than for
higher levels). The difference between the two would be essentially that if you
divide by mean value, things with a large relative SD will tend to dominate the
variations in 'distance', whereas if you centre and divide by SD, that won't
happen to the same extent. But which option is more useful is hard to predict.
Me, I think I'd try both and see which made most sense.
Incidentally, scaling by mean value without centring using scale() would
probably look something like
x.scaled <- scale(x, center=FALSE, scale=apply(x,2,mean))
assuming x has columns corresponding to your measurements and
dist(x.scaled)
then gives you your distance matrix.
Steve E
lab of the Government Chemist
UK
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