 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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