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. ------------------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================