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 .
|
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
(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()