self start for Beta growth function with four parameters
Self starter for Beta Growth function with parameters w.max, t.e, t.m and t.b
bgf4(time, w.max, t.e, t.m, t.b) SSbgf4(time, w.max, t.e, t.m, t.b)
time |
input vector (x) which is normally ‘time’. |
w.max |
value of weight or mass at its peak. |
t.e |
time at which the weight or mass reaches its peak. |
t.m |
time at which half of the maximum weight or mass has been reached. |
t.b |
time at which growth starts. |
For details see the publication by Yin et al. (2003) “A Flexible Sigmoid Function of Determinate Growth”.
This is a difficult function to fit because the linear constrains are not explicitly introduced
in the optimization process. See function SSbgrp for a reparameterized version.
This is equation 11 (pg. 368) in the publication by Yin, but with correction (https://doi.org/10.1093/aob/mcg091) and with ‘w.b’ equal to zero.
a numeric vector of the same length as x (time) containing parameter estimates for equation specified
bgf4: vector of the same length as x (time) using the beta growth function with four parameters
data(sm)
## Let's just pick one crop
sm2 <- subset(sm, Crop == "M")
fit <- nls(Yield ~ SSbgf4(DOY, w.max, t.e, t.m, t.b), data = sm2)
plot(Yield ~ DOY, data = sm2)
lines(sm2$DOY,fitted(fit))
## For this particular problem it could be better to 'fix' t.b and w.b
fit0 <- nls(Yield ~ bgf2(DOY, w.max, w.b = 0, t.e, t.m, t.b = 141),
data = sm2, start = list(w.max = 16, t.e= 240, t.m = 200))
x <- seq(0, 17, by = 0.25)
y <- bgf4(x, 20, 15, 10, 2)
plot(x, y)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.