statforbiology (version 0.9.9)

SSlorentz: Lorentz equation

Description

These functions provide the Lorentz equation with 3 and 4 parameters ('lorentz.3.fun()' and 'lorentz.4.fun()' ), as well as the self-starters for the nls function ( 'NLS.lorentz.3()' and 'NLS.lorentz.4()') and for the drm function in the 'drc' package ('DRC.lorentz.3()' and 'DRC.lorentz.4()')

Usage

lorentz.3.fun(X, b, d, e)
lorentz.4.fun(X, b, c, d, e)
NLS.lorentz.3(X, b, d, e)
NLS.lorentz.4(X, b, c, d, e)
DRC.lorentz.3()
DRC.lorentz.4()

Value

lorentz.3.fun(), lorentz.4.fun(), NLS.lorentz.3() and NLS.lorentz.4() return a numeric value, while DRC.lorentz.3() and DRC.lorentz.4() returns a list containing the nonlinear function, the self starter function and the parameter names.

Arguments

X

a numeric vector of values at which to evaluate the model

b

model parameter

d

model parameter

e

model parameter

c

model parameter

Author

Andrea Onofri

Details

These functions provide the Lorentz equation, that is a bell-shaped curve similar to a gaussian density function. It is parameterised as:

$$ f(x) = c + \frac{d - c} {( 1 + b \, (X - e)^2) } $$

The parameter 'e' represents the abscissa of the maximum value, while c is the minimum (asymptotic) response value and d is the maximum response value. The parameter 'b' relates to the slope at inflection point. For the 3-parameters curve, c is equal to 0.

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/

Examples

X <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50)
Y1 <- c(0.1, 2, 5.7, 9.3, 19.7, 28.4, 20.3, 6.6, 1.3, 0.1)
Y2 <- Y1 + 2

# nls fit
mod.nls <- nls(Y1 ~ NLS.lorentz.3(X, b, d, e) )
mod.nls2 <- nls(Y2 ~ NLS.lorentz.4(X, b, c, d, e) )

# drm fit
mod.drc <- drm(Y1 ~ X, fct = DRC.lorentz.3() )
mod.drc2 <- drm(Y2 ~ X, fct = DRC.lorentz.4() )
plot(mod.drc, ylim = c(0, 30), log = "")
plot(mod.drc2, add = TRUE, col = "red")