statforbiology (version 0.9.9)

SSW2: Weibull equation (Type II)

Description

These functions provide the Weibull equation (type II), that has an asymmetric sygmoidal shape and it has been used for bioassay work. These functions provide the 4-, 3- and 2-parameter equations (W2.4.fun(), W2.3.fun() and W2.2.fun()) as well as the self-starters for the nls function (NLS.W2.4(), NLS.W2.3() and NLS.W2.2()

Usage

W2.4.fun(predictor, b, c, d, e)
W2.3.fun(predictor, b, d, e)
W2.2.fun(predictor, b, e)
NLS.W2.4(predictor, b, c, d, e)
NLS.W2.3(predictor, b, d, e)
NLS.W2.2(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 inlection point)

Author

Andrea Onofri

Details

These functions provide the Weibull (Type I) equation for bioassay work This equation (4-parameters) is parameterised as: $$ f(x) = c + (d - c) (1 - \exp( - \exp (b \, (\log(x) - \log(e))))) $$ 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

library(statforbiology)
dataset <- getAgroData("brassica")
model <- nls(FW ~ NLS.W2.4(Dose, b, c, d, e), data = dataset)
model <- nls(FW ~ NLS.W2.3(Dose, b, d, e), data = dataset)
model <- nls(FW/max(FW) ~ NLS.W2.2(Dose, b, e), data = dataset)
summary(model)