On Feb 2, 2008 2:28 PM, Ben Abbott <address@hidden> wrote:
Regarding "scale x unconditionally", do you refer to the scaling used
by wpolyfit;
(x - mean (x)) / std (x)
or to Thomas' suggestion to just scale the magnitude?
x / max (x)
I mean Thomas' suggestion. That is to be precise x / max(abs(x))
If you refer to Thomas' suggestion, the maximum value will result in
as much trouble/benefit as the minimum value.
No. If your data are well centered, the min(abs(x)) ~ eps, so
scaling to
min does not work. In case of data having a large offset,
min(abs(x)) ~ max(abs(x)) ~ mean(abs(x)), so scaling to any of these
numbers would be equally helpful. But scaling to max(abs(x)) would
guarantee
to make all the data in (-1,1) range in all cases and that should help
with numerical precision.
Perhaps a better solution would be (a) the geometric mean of the
magnitudes, (b) the median of the magnitudes, (c) the mean of the
magnitudes, (d) consider several normalization options and select the
most numerically stable one.
See above. I doubt that the fit will be that sensitive to the scaling
parameter, i.e. to say instead of max(abs(x)) you can use
0.5*max(abs(x))
and you probably will not see much of a difference.
Using some more sofisticated approximation is to make some
assumption of
the data distribution and we do not want to do that in a generic
function.
In any event, what should be done about s.R and s.X? Are they to
represent the scaled dependent variable?
I do not know.