On Thu, 20 Dec 2001, Johannes Hartig wrote:
> Does anyone know the original applications
> or the "meaning" of the "S"-function in SPSS?
> I know the function itself:
> Y = e**(b0 + (b1/t)) or
> ln(Y) = b0 + (b1/t)
> and I know how the curve looks like, but I am wondering in which
> fields of research this function is typically used and which empirical
> relations it describes?
You may find it looks a little more like other functions you have seen
somewhere if you rewrite it as
Y = a*e**(b1), or equivalently
ln(Y) = ln(a) + b1
When it is desired to find the value of "a", it is simply e**(b0),
from your equation above.
In biological contexts, this describes an exponential growth curve
(which applies to some period of almost any organism's life, usually
its extreme youth, before environmental constraints restrict its growth
rate). Then the parameter "b1" is positive and is intimately connected
to "doubling time", the length of time during which the organism doubles
in size. I suspect that this is why your original formulation had "b1/t"
in the exponent.
If "b1" is negative, then the equation models exponential decay, and the
parameter "b1" is connected (in exactly the same way as above) to
"half-life". Applications include (perhaps obviously) the diminution
over time of the radioactivity of a radioactive substance.
- DFB.
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