Description Usage Arguments Details Value Note Author(s) References See Also Examples
'cedergreen' provides a very general way of specifying then Cedergreen-Ritz-Streibig modified log-logistic model for describing hormesis, under various constraints on the parameters.
CRS.6
is the extension of link{cedergreen}
with freely varying alpha parameter.
For u-shaped hormesis data 'ucedergreen' provides a very general way of specifying the Cedergreen-Ritz-Streibig modified log-logistic model, under various constraints on the parameters.
1 2 3 4 5 6 7 8 9 10 11 12 13 | cedergreen(fixed = c(NA, NA, NA, NA, NA),
names = c("b", "c", "d", "e", "f"),
method = c("1", "2", "3", "4"), ssfct = NULL,
alpha, fctName, fctText)
CRS.6(fixed = c(NA, NA, NA, NA, NA, NA),
names = c("b","c","d","e","f","g"),
method = c("1", "2", "3", "4"), ssfct = NULL)
ucedergreen(fixed = c(NA, NA, NA, NA, NA),
names = c("b", "c", "d", "e", "f"),
method = c("1", "2", "3", "4"), ssfct = NULL,
alpha)
|
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters (should not contain ":"). The order of the parameters is: b, c, d, e, f (see under 'Details'). |
method |
character string indicating the self starter function to use. |
ssfct |
a self starter function to be used. |
alpha |
numeric value between 0 and 1, reflecting the steepness of the hormesis peak. This argument needs to be specified. |
fctName |
optional character string used internally by convenience functions. |
fctText |
optional character string used internally by convenience functions. |
The model is given by the expression
f(x) = c + \frac{d-c+f exp(-1/(x^{α}))}{1+exp(b(log(x)-log(e)))}
which is a five-parameter model (alpha is fixed or freely varying). Not all features (eg EC/ED calculation) are available for the model with freely varying alpha.
It is a modification of the four-parameter logistic curve to take hormesis into account.
The u-shaped model is given by the expression
f(x) = cd - \frac{d-c+f \exp(-1/x^{α})}{1+\exp(b(\log(x)-\log(e)))}
The value returned is a list containing the non-linear function, the self starter function and the parameter names.
The functions are for use with the functions drm
.
Christian Ritz
Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, Environmental Toxicology and Chemistry 24, 3166–3172.
For fixed alpha, several special cases are handled by the following convenience functions
CRS.4a
, CRS.4b
,
CRS.4c
, CRS.5a
, CRS.5b
, CRS.5c
,
UCRS.4a
, UCRS.4b
, UCRS.4c
, UCRS.5a
,
UCRS.5b
, UCRS.5c
where a, b and c correspond to
the pre-specified alpha values 1, 0.5 and 0.25, respectively.
1 2 3 4 |
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.