SSrichards {richards}R Documentation

Richards Function Model

Description

This selfStart model evaluates the Richards function and its gradient, for ny different from 0. It has an initial attribute that will evaluate initial estimates of the parameters a, d, b, and x50 for a given set of data for ny set to 1.

Usage

             SSrichards(input, a, d, b,     x50, ny)
            SSrichardsE(input, a, d, b,       e, ny)
          SSrichardsLog(input, a, d, xmid, scal, ny)
        SSrichardsLogBM(input, a, d, xmid,    b,  m)

Arguments

input a numeric vector of values at which to evaluate the model.
a a numeric parameter representing the horizontal asymptote on the left side (very small values of input) for b positive, else the horizontal asymptote on the right side.
d a numeric parameter representing the horizontal asymptote on the right side (very large values of input) for b positive, else the horizontal asymptote on the left side.
b a numeric scale parameter on the input axis, the 'growth rate', the reciprocal of the scale parameter scal for the four point logistic curve by SSfpl.
x50 a numeric parameter representing the input value at the inflection point (for ny = 1) of the curve. The value of SSrichards will be midway between a and d at x50.
e the parameter determine the input value at the inflection point of the curve.
ny the fifth parameter: affects near which asymptote maximum 'growth' occurs.
m the fifth parameter: affects near which asymptote maximum 'growth' occurs. Reciprocal of ny. (Note that the m of Richards (1959) is k with ny = k - 1.)
xmid a numeric parameter representing the input value at the inflection point (for ny = 1) of the curve. The value of SSrichardsLog will be midway between a and d at xmid.
scal a numeric scale parameter on the input axis, 'growth rate'.

Details

Why the 4 versions?

The version SSrichardsE (and mainly SSrichards) was made to be close to the usual parameterization of the four-parameter logistic curve at Statens Serum Institute.

SSrichardsLog and SSrichardsLogBM was made during writing of this documentation. SSrichardsLog is closer to other selfStart methods implemented in R. For SSrichardsLogBM bounds on the parameter b can be avioded.

Value

a numeric vector of the same length as input. It is the value of the expression
SSrichards: d + (a - d) / (1 + (2^ny-1) * (input/x50)^b)^(1/ny)
if 1 + (2^ny-1) * (input/x50)^b > 0,
else d,
SSrichardsE: d + (a - d) / (1 + ny * (input/e)^b)^(1/ny),
if 1 + ny * (input/e)^b > 0,
else d,
SSrichardsLog: d + (a - d) / (1 + (2^ny-1) * exp((input-xmid)/scal))^(1/ny)
if 1 + (2^ny-1) * exp((input-xmid)/scal) > 0,
else d, or
SSrichardsLogBM: d + (a - d) / (1 + (2^(1/m)-1) * exp(b*(input-xmid)))^m
if 1 + (2^(1/m)-1) * exp(b*(input-xmid)) > 0,
else d.

See richards about details of the function. Observe that the selfStarts models SSrichards, SSrichardsE, and SSrichardsLog does not handle the Gompertz function. See also richards about the modified selfStarts with constant asymptote on the right side (b positive) after reaching this asymptote.
If all of the arguments a, d, b (scal), x50 (xmid), and ny are names of objects, the gradient matrix with respect to these names is attached as an attribute named gradient.

Author(s)

Jens Henrik Badsberg

Examples

 

demo(contourModified)


# make3plots()

[Package richards version 0.4 Index]