| SSrichards {richards} | R Documentation |
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.
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)
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'. |
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.
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. |
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.
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.
Jens Henrik Badsberg
demo(contourModified) # make3plots()