statforbiology (version 0.9.9)

SSLL: Log-logistic equation

Description

These functions provide the loglogistic equation, that has a symmetric sygmoidal shape over the logarithm of time and it has been used for bioassay work. These functions provide the 4-, 3- and 2-parameter equations (LL4.fun(), LL3.fun() and LL2.fun()) as well as the self-starters for the nls function (NLS.LL4(), NLS.LL3() and NLS.LL2() )

Usage

LL4.fun(predictor, b, c, d, e)
LL3.fun(predictor, b, d, e)
LL2.fun(predictor, b, e)
NLS.LL4(predictor, b, c, d, e)
NLS.LL3(predictor, b, d, e)
NLS.LL2(predictor, b, e)

Value

All these functions return a numeric value

Arguments

predictor

a numeric vector of values at which to evaluate the model

b

model parameter (slope at inflection point)

c

model parameter (lower asymptote)

d

model parameter (higher asymptote)

e

model parameter (abscissa at inflection point)

Author

Andrea Onofri

Details

These functions provide the log-logistic equation for bioassay work This equation (4-parameters) is parameterised as: $$ f(x) = c + \frac{d - c}{\exp ( 1 + \exp ( - b\,(\log(x) - \log(e))))} $$ For the 3- and 2-parameters model, c is equal to 0, while for the 2-parameter model d is equal to 1.

References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.

Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

Ritz, C., Jensen, S.M., Gerhard, D., Streibig, J.C., 2019. Dose-response analysis using R, CRC Press. ed. USA.

Examples

dataset <- getAgroData("brassica")

model <- nls(FW ~ NLS.LL4(Dose, b, c, d, e), data = dataset)
model <- nls(FW ~ NLS.LL3(Dose, b, d, e), data = dataset)
model <- nls(FW/max(FW) ~ NLS.LL2(Dose, b, e), data = dataset)
summary(model)