[R] non-linear normalization of data

cstrato@EUnet.at cstrato at EUnet.at
Fri Sep 15 19:54:39 CEST 2000

Dear R/S users

I hope the answer to this question turns out to be simple, since the
question can be formulated in a simple way:
If I have a sausage which is curved, which transformation do I need
to apply to straigthen it out?

More concretely:
Let an experiment produce 1,000 data points with every point in
the range(1, 10,000) and let us assume a gaussian distribution.
Now I repeat the experiment 8 times.

For every data point I get a mean with standard deviation. Due to
experimental limits, data points with low values have usually a
higher standard deviation.

If I draw the data of any two experiments on a Log-Log-plot, the
data will be scattered around the diagonal.

If e.g. an instrument has a lower sensitivity, the cloud seen in the
scatterplot would be shifted and/or rotated. To correct for this
I could do a linear transformation such as e.g. "lsfit" or "ltsreg".
(is this correct?)

However, when the instrument introduces some kind of non-
linearity, e.g. saturation effects at high values, so that the
data look like a curved sausage in 8-dim space, what is the best
way to fit these data?

Thank you in advance for your help
Best regards
Christian Stratowa, Vienna, Austria

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