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) SSrichardsLogBG(input, a, d, xmid, b, g)
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.
(The 'growth' parameter b should be negative, and a
is thus the right side (larger) asymptote, for Bertalenffy growth models.)
|
x50 |
a numeric parameter representing the input value at
the center 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 shape parameter: affects near which asymptote maximum 'growth' occurs. |
g |
the reciprocal of the shape parameter: affects near which
asymptote maximum 'growth' occurs. Reciprocal of ny . |
xmid |
a numeric parameter representing the input value at
the center 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. This is also the source of the sign of b
.
SSrichardsLog
and SSrichardsLogBM
was made during writing of this
documentation.
SSrichardsLog
is closer to other selfStart
methods implemented in R.
For SSrichardsLogBG
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 |
|
SSrichardsLogBG: | d + (a - d) / (1 + (2^(1/g)-1) * exp(b*(input-xmid)))^g |
if 1 + (2^(1/g)-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
(m
) 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()