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Dec 14, 2016

Growth rate parameter for nonlinear 3P logistic function

I have a dataset of plant stem length measured at weekly intervals and want to fit a 3P logistic curve to each subject (plant). The JMP 12 Pro output for the nonlinear platform provides infection point, growth rate (slope of the tangent at the inflection point, as I understand it) and upper asymtope for each curve fit. The magnitude of the growth rate is not in line with the slope of the curve, however. According to Winsor (1932) maximum growth rate = bk/4, where k=upper asymptote and b is an estimated quantity associated with the slope. If I insert the "growth rate" estimate from JMP for b into the above equation, I get a quantity closer to the actual slope that I would expect, which in my case is cm of stem growth per day. Therefore when reporting the quantity for b, I don't think it is valid to call it "growth rate" because it is not the actual slope of the tangent at the inflection point. What is an acceptable name for the quantity b?