nlraa (version 1.9.7)

SSbgrp: self start for the reparameterized Beta growth function

Description

Self starter for Beta Growth function with parameters w.max, lt.m and ldt

Usage

bgrp(time, w.max, lt.e, ldt)
SSbgrp(time, w.max, lt.e, ldt)

Value

bgrp: vector of the same length as x (time) using the beta growth function (reparameterized).

Arguments

time

input vector (x) which is normally ‘time’, the smallest value should be close to zero.

w.max

value of weight or mass at its peak

lt.e

log of the time at which the maximum weight or mass has been reached.

ldt

log of the difference between time at which the weight or mass reaches its peak and half its peak (\(log(t.e - t.m)\)).

Details

For details see the publication by Yin et al. (2003) “A Flexible Sigmoid Function of Determinate Growth”. This is a reparameterization of the beta growth function with guaranteed constraints, so it is expected to behave numerically better than SSbgf.

The form of the equation is: $$w.max * (1 + (exp(lt.e) - time)/exp(ldt)) * (time/exp(lt.e))^(exp(lt.e) / exp(ldt))$$. Given this function weight is expected to decay and reach zero again at \(2*ldt\). This is a reparameterized version of the Beta-Growth function in which the parameters are unconstrained, but they are expressed in the log-scale.

Examples

# \donttest{
require(ggplot2)
x <- 1:30
y <- bgrp(x, 20, log(25), log(5)) + rnorm(30, 0, 1)
dat <- data.frame(x = x, y = y)
fit <- nls(y ~ SSbgrp(x, w.max, lt.e, ldt), data = dat)
## We are able to recover the original values
exp(coef(fit)[2:3])
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))
# }