Description Usage Arguments Details Value Note Author(s) References See Also
lnormal
and the accompanying convenience functions provide a general framework for specifying
the mean function of the decreasing or incresing log-normal dose-response model.
1 2 3 4 5 6 7 8 9 10 11 | lnormal(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"),
method = c("1", "2", "3", "4"), ssfct = NULL,
fctName, fctText, loge = FALSE)
LN.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)
LN.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)
LN.3u(upper = 1, fixed = c(NA, NA, NA), names = c("b", "c", "e"), ...)
LN.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
|
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
vector of character strings giving the names of the parameters (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e, f (see under 'Details' for the precise meaning of each parameter). |
method |
character string indicating the self starter function to use. |
ssfct |
a self starter function to be used. |
fctName |
character string used internally by convenience functions (optional). |
fctText |
character string used internally by convenience functions (optional). |
loge |
logical indicating whether or not ED50 or log(ED50) should be a parameter in the model. By default ED50 is a model parameter. |
upper |
numeric specifying the upper horizontal asymptote in the convenience function. The default is 1. |
... |
additional arguments to be passed from the convenience functions to |
For the case where log(ED50), denoted e in the equation below, is a parameter in the model, the mean function is:
f(x) = c + (d-c)(Φ(b(\log(x)-e)))
and the mean function is:
f(x) = c + (d-c)(Φ(b(\log(x)-\log(e))))
in case ED50, which is also denoted e, is a parameter in the model. If the former model is fitted any estimated ED values will need to be back-transformed subsequently in order to obtain effective doses on the original scale.
The mean functions above yield the same models as those described by Bruce and Versteeg (1992), but in a different parameterisations (among other things the natural logarithm is used).
For the case c=0 and d=1, the log-normal model reduces the classic probit model (Finney, 1971)
with log dose as explanatory variable (mostly used for quantal data). This special case is available through
the convenience function LN.2
.
The case c=0 is available as the function LN.3
, whereas the LN.3u
corresponds to the special
case where the upper horizontal asymptote is fixed (default is 1). The full four-parameter model is available
through LN.4
.
The value returned is a list containing the non-linear function, the self starter function and the parameter names.
The function is for use with the function drm
, but typically the convenience functions
link{LN.2}
, link{LN.3}
, link{LN.3u}
, and link{LN.4}
should be used.
Christian Ritz
Finney, D. J. (1971) Probit analysis, London: Cambridge University Press.
Bruce, R. D. and Versteeg, D. J. (1992) A statistical procedure for modeling continuous toxicity data, Environ. Toxicol. Chem., 11, 1485–1494.
The log-logistic model (llogistic
) is very similar to the log-normal model at least in the middle,
but they may differ in the tails and thus provide different estimates of low effect concentrations EC/ED.
Examples are provided in the help pages of the datasets S.capricornutum
, P.promelas
,
and M.bahia
.
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