On Fri, 4 Aug 2000, Charles Paxton wrote:
> I have a curve of cumulative number of species over time (i.e. time,
> years in fact on x). For theoretical reasons I want to fit a two
> parameter rectangular hyperbola of the form Y=(A*X)/(B+X) where A and
> B are constants. ...
> The problem as I see it is that my Y variables are not independent of
> each other as obviously cumulative scores build on each other. Thus
> generating estimates for my parameters and confidence intervals is
> problematical.
I do not see that estimating the parameters is a problem, at least not a
problem associated with non-independence of observations. If there is a
problem, it would affect the confidence intervals. But whether there is
a problem depends on how the values observed are observed. If the number
of species at time t+1 is observed by taking the number of species
observed at time t and adding to that the number of new species that
have been observed (or that have evolved?) since time t, I will agree
that the data contain clear dependencies. But if the number of species
at time t+1 is obtained by a count made at that time, it seems to me
that the _count_ at time t+1 could well be independent of the _count_
at time t. (Then the difference in counts would represent the number of
new species generated in the interval, minus the number of species that
have become extinct in the interval, plus errors of observation (mostly
in the form of species existing at each time but for one reason or
another not observed, or at any rate not counted.)
(Colleagues who know more than I do about species generation and
extinction will doubtless correct any egregious errors in the foregoing!)
You gave your model above as Y = (A*X)/(B+X).
Presumably you estimate the parameters A and B by taking reciprocals?
Let y = 1/Y, x = 1/X, then y = a + b*x
and a = 1/A, b = B/A.
(Unless, of course, you really need to minimize squared
deviations from Y^ instead of (1/Y)^.)
> I need the actual value of the parameters.
> Any thoughts or pointers to text books?
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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