SS_BC3: The Brain-Cousens hormesis models

In OnofriAndreaPG/aomisc: Statistical methods for the agricultural sciences

The Brain-Cousens hormesis models

Description

These functions provide the Brain-Cousens models for describing u-shaped hormesis. They can be used with 'nls()' or 'nlme()' or 'gnls()' and they do not contain self-starting routines.

Usage

  BC.5.fun(predictor, b, c, d, e, f)
  BC.4.fun(predictor, b, d, e, f)
  BC.3.fun(predictor, b, e, f)

Arguments

predictor	a numeric vector of values at which to evaluate the model
b	model parameter: slope near to the inflection point
c	model parameter: lower asymptote
d	model parameter: higher asymptote
e	model parameter: dose at inflection point
f	model parameter for hormesis

Details

The model functions for the Brain-Cousens model (Brain and Cousens, 1989) is

f(x, b,c,d,e,f) = c + \frac{d-c+fx}{1+\exp(b(\log(x)-\log(e)))}

,

f(x, b,d,e,f) = c + \frac{d+fx}{1+\exp(b(\log(x)-\log(e)))}

,

f(x, b,e,f) = c + \frac{1+fx}{1+\exp(b(\log(x)-\log(e)))}

, These functions do not provide a selfStarting routine, but you can obtain starting values from a drc fit, by using the corresponding functions BC.4() and BC.5().

Value

These functions return a numeric value

Author(s)

Andrea Onofri

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/ Brain, P. and Cousens, R. (1989) An equation to describe dose responses where there is stimulation of growth at low doses, Weed Research, 29, 93–96.

Examples

X <- c(1, 3, 5, 7, 9, 11, 13, 20)
Y <- c(8.22, 14.0, 17.2, 16.9, 19.2, 19.6, 19.4, 19.6)

# nls fit
model <- nls(Y ~ NLS.asymReg(X, init, m, plateau) )

# drm fit
model <- drm(Y ~ X, fct = DRC.asymReg())
summary(model)

model2 <- drm(Y ~ X, fct = DRC.SSasymp())
summary(model2)

OnofriAndreaPG/aomisc documentation built on Feb. 26, 2024, 8:21 p.m.