SS_monoexp3(): Creates initial coefficient estimates for a selfStart
model for a 3-parameter monoexponential() function (A, B, tau).
SS_monoexp4() supports a 4-parameter monoexponential() function
(A, B, tau, TD).
Arguments
- t
A numeric vector of the predictor variable; time or sample number.
- A
A numeric parameter for the starting (baseline) value of the response variable.
- B
A numeric parameter for the ending (asymptote) value of the response variable.
- tau
A numeric parameter for the time constant
tau(\(\tau\)) of the exponential curve, in units of the predictor variablet.- TD
A numeric parameter for the time delay before the onset of exponential response, in units of the predictor variable
t.
Value
SS_monoexp3() and SS_monoexp4(): A numeric vector of predicted values the same
length as the predictor variable t.
Details
For 3-parameter model: y ~ SS_monoexp3(t, A, B, tau)
For 4-parameter model: y ~ SS_monoexp4(t, A, B, tau, TD)
The 3-parameter model is recommended for small samples or when no obvious time delay exists, as it converges more reliably.
Examples
set.seed(13)
t <- 1:60
## create an exponential curve with random noise
x <- monoexponential(t, A = 10, B = 100, tau = 8, TD = 15) + rnorm(length(t), 0, 3)
data <- data.frame(t, x)
(model <- nls(x ~ SS_monoexp4(t, A, B, tau, TD), data = data))
#> Nonlinear regression model
#> model: x ~ SS_monoexp4(t, A, B, tau, TD)
#> data: data
#> A B tau TD
#> 10.461 100.233 8.313 14.884
#> residual sum-of-squares: 455.5
#>
#> Number of iterations to convergence: 5
#> Achieved convergence tolerance: 7.481e-07
y <- predict(model, data)
library(ggplot2)
ggplot(data, aes(t, x)) +
theme_mnirs() +
geom_point() +
geom_line(aes(y = y))
