newton {Bhat} R Documentation

## Function minimization with box-constraints

### Description

Newton-Raphson algorithm for minimizing a function f over the parameters specified in the input list x. Note, a Newton-Raphson search is very efficient in the 'quadratic region' near the optimum. In higher dimensions it tends to be rather unstable and may behave chaotically. Therefore, a (local or global) minimum should be available to begin with. Use the optim or dfp functions to search for optima.

### Usage

newton(x, f, eps = 0.1, itmax = 10, relax = 0, nfcn = 0)


### Arguments

 x a list with components 'label' (of mode character), 'est' (the parameter vector with the initial guess), 'low' (vector with lower bounds), and 'upp' (vector with upper bounds) f the function that is to be minimized over the parameter vector defined by the list x eps converges when all (logit-transformed) derivatives are smaller eps itmax maximum number of Newton-Raphson iterations relax numeric. If 0, take full Newton step, otherwise 'relax' step incrementally until a better value is found nfcn number of function calls

### Value

list with the following components:

 fmin the function value f at the minimum label the labels est a vector of the parameter estimates at the minimum. newton does not overwrite x low lower 95% (Wald) confidence bound upp upper 95% (Wald) confidence bound

The confidence bounds assume that the function f is a negative log-likelihood

### Note

newton computes the (logit-transformed) Hessian of f (using logit.hessian). This function is part of the Bhat exploration tool

### Author(s)

E. Georg Luebeck (FHCRC)

dfp, ftrf, btrf, logit.hessian, plkhci

### Examples


# generate some Poisson counts on the fly
dose <- c(rep(0,100),rep(1,100),rep(5,100),rep(10,100))
data <- cbind(dose,rpois(400,20*(1+dose*.5*(1-dose*0.05))))

# neg. log-likelihood of Poisson model with 'linear-quadratic' mean:
lkh <- function (x) {
ds <- data[, 1]
y  <- data[, 2]
g <- x[1] * (1 + ds * x[2] * (1 - x[3] * ds))
return(sum(g - y * log(g)))
}

# for example define
x <- list(label=c("a","b","c"),est=c(10.,10.,.01),low=c(0,0,0),upp=c(100,20,.1))

# calls:
r <- dfp(x,f=lkh)
x$est <- r$est
results <- newton(x,lkh)



[Package Bhat version 0.9-12 Index]