Hello,
I am trying to plot confidence bands on the mean and prediction bands for the
following
nonlinear regression, using maximum likelihood via optim. A toy example with
data and
code of what I am trying to accomplish is:
VOL<-c(0.01591475, 1.19147935 ,6.34102460, 53.68809287, 91.90143074,
116.21397007,
146.41843056, 215.64535337, 256.53149673, 315.73609232)
Age <-c(1.622222, 2.833333 , 3.927778, 7.150000, 8.166667,
8.752778 , 9.444444, 10.797222 ,11.725000, 12.775000)
with that I fit the following likelihood function
loglik <- function(param, x, y)
{
b0 <- param[1]
b1 <- param[2]
sigma <- param[3]
res <- dnorm(y, b0*exp(b1/x), sigma, log= T)
.value <- sum(res)
}
regression <- optim(par = c(800,-2,.2),
fn = loglik,
method = "L-BFGS-B",
lower = c(-Inf, -Inf, 1e-10),
control = list(fnscale = -1),
x = Age,
y = VOL,
hessian = T)
confint.par <- sqrt(diag(solve(regression$hessian *-1)))
now that I have confidence intervals for each parameter, how can a draw
confidence
bands for the mean regression line?
Any help will be appreciated.
Cristián Montes
Site Productivity Division Head
Bioforest S.A.
Chile.
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