I've been discussing this thread with my colleague Bill Knight,
and in particular sent him the summary that was posted yesterday
by Peter Scherer. (Bill is not a subscriber to this list.)
Bill has asked me to post the following response to some points
in the summary. Since Bill is not a subscriber, any rejoinders
should be sent directly to Bill
knight@math.unb.ca
rather than (or in addition) to this list.
cheers,
Rolf Turner
rolf@math.unb.ca
===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===+===
On Fri, 15 Sep 2000 12:49, "Peter Scherer <pscherer@dowagro.com> wrote
> Subject: [S] Summary - SAS does; S-Plus doesn't
> . . . . . . . . . . . . . . [cut]. . . . . . . . . . . . . . . . .
> A secondary question posted in my original message concerned the
> appropriateness of including the "time zero" point in the regression
> when that point has been defined to be 100 (or any given value) and
> then forcing the model through that point. Understanding that there
> are situation specific exceptions, the general counsel has been to
> exclude this point as it really provides no additional information and
> artificially inflates degrees of freedom.
> . . . . . . . . . . . . . . [cut]. . . . . . . . . . . . . . . . .
Although this "general counsel" was my original reaction also,
it's wrong if the model is
observation = function(day, parameters) + error ,
with the usual independent normal errors - zero mean, same variance --
and this is transformed to,
100 * observation 100*[ function(day, parameters) + error]
--------------------- = ----------------------------------------
(initial observation) (initial observation) ,
which is then fitted. Of course the members of
(error vector)/(initial observation)
are not independent. One should fit the untransformed data first, then
scale "function(0,parameters)" to 100 -- rather than scale to 100, then
fit.
Usually when scaling, say meters to feet or ounces to grams,
it's obvious that the scaling shouldn't change the analysis. I
guess that this scaling being data dependent muddies the waters,
perhaps because the units are artificial rather than good old
feet, grams, kilopascals, etc.
Bill Knight
knight@unb.ca
http://www.math.unb.ca/~knight
Postscript:
The above assumes that measurement error is the dominant source
of variability. A couple of plausible alternatives -----
(1) Error standard deviation is proportional to expectation
which suggests a weighted regression or logarithmic transformation.
(2) The process of soil degradation is a Markov process whose
variability dominates variability of measurement error, which case
it's more appropriate to fit differences (or ratios) of successive
observations, and there is no problem with the frozen point.
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