newton {Bhat} | R Documentation |
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.
newton(x, f, eps=0.1, itmax=10, relax=0, nfcn=0)
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 |
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
newton
computes the (logit-transformed) Hessian of f
(using logit.hessian). This function is part of the Bhat exploration
tool
E. Georg Luebeck (FHCRC)
dfp
, ftrf
, btrf
, logit.hessian
, plkhci
# 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)