SSprofd {nlraa}

self start for profile decay function

Description

Self starter for a decay of a variable within a canopy (e.g. nitrogen concentration).

Usage

profd(x, a, b, c, d)

SSprofd(x, a, b, c, d)

Arguments

x

input vector (x)

a

represents the maximum value

b

represents the minimum value

c

represents the rate of decay

d

represents an empirical coefficient which provides flexibility

Details

This function is described in Archontoulis and Miguez (2015) - (doi:10.2134/agronj2012.0506) and originally in Johnson et al. (2010) Annals of Botany 106: 735–749, 2010. (doi:10.1093/aob/mcq183).

Value

a numeric vector of the same length as x containing parameter estimates for equation specified

profd: vector of the same length as x using the profd function

Examples

require(ggplot2)
set.seed(1234)
x <- 1:10
y <- profd(x, 0.3, 0.05, 0.5, 4) + rnorm(10, 0, 0.01)
dat <- data.frame(x = x, y = y)
fit <- nls(y ~ SSprofd(x, a, b, c, d), data = dat)
## plot
ggplot(data = dat, aes(x = x, y = y)) + 
  geom_point() + 
  geom_line(aes(y = fitted(fit)))
## profiling
## It does not work at a lower alphamax level
## Use this if you want to look at all four parameters
## par(mfrow=c(2,2))
plot(profile(fit, alphamax = 0.016))
## Reset graphical parameter as appropriate: par(mfrow=c(1,1))
## parameter 'd' is not well constrained
confint(fit, level = 0.9)