maxLik (version 0.6-0)

maxBFGS: BFGS, SANN and Nelder-Mead Maximization

Description

These functions are wrappers for optim where the arguments are compatible with maxNR

Usage

maxBFGS(fn, grad = NULL, hess=NULL, start, print.level = 0,
iterlim = 200,
constraints,
   tol = 1e-08, reltol=tol, ... )
maxSANN(fn, grad = NULL, hess = NULL, start, print.level = 0, iterlim =
   10000,
   constraints,
   tol = 1e-08, reltol=tol, temp = 10, tmax = 10, parscale = rep(1, length = length(start)), ...)
maxNM(fn, grad = NULL, hess = NULL, start, print.level = 0, iterlim =
   500,
constraints,
tol = 1e-08, reltol=tol, parscale = rep(1, length = length(start)), alpha = 1, beta = 0.5, gamma = 2, ...)

Arguments

fn

function to be maximised. Must have the parameter vector as the first argument. In order to use numeric gradient and BHHH method, fn must return vector of observation-specific likelihood values. Those are summed by maxNR if

grad

gradient of the function. Must have the parameter vector as the first argument. If NULL, numeric gradient is used (only maxBFGS uses gradient). Gradient may return a matrix, where columns correspond to the parameters and rows t

hess

Hessian of the function. Not used by any of these methods, for compatibility with maxNR.

start

initial values for the parameters.

print.level

a larger number prints more working information.

iterlim

maximum number of iterations.

constraints

either NULL for unconstrained optimization or a list with two components. The components may be either eqA and eqB for equality-constrained optimization $A \theta + B = 0$; or ineqA and

tol, reltol

the relative convergence tolerance (see optim). tol is for compatibility with maxNR.

temp

controls the '"SANN"' method. It is the starting temperature for the cooling schedule. Defaults to '10'.

tmax

is the number of function evaluations at each temperature for the '"SANN"' method. Defaults to '10'. (see optim)

parscale

A vector of scaling values for the parameters. Optimization is performed on 'par/parscale' and these should be comparable in the sense that a unit change in any element produces about a unit change in the scaled value. (see

alpha, beta, gamma

Scaling parameters for the '"Nelder-Mead"' method. 'alpha' is the reflection factor (default 1.0), 'beta' the contraction factor (0.5) and 'gamma' the expansion factor (2.0). (see optim

...

further arguments for fn and grad.

Value

• Object of class "maxim":
• maximum
  value of fn at maximum.
• estimate
  best set of parameters found.
• gradient
  gradient at parameter value estimate.
• hessian
  value of Hessian at optimum.
• code
  integer. Success code, 0 is success (see optim).
• message
  character string giving any additional information returned by the optimizer, or NULL.
• activePar
  logical vector indicating which parameters are treated as free (currently all parameters).
• iterations
  two-element integer vector giving the number of calls to fn and gr, respectively. This excludes those calls needed to compute the Hessian, if requested, and any calls to fn to compute a finite-difference approximation to the gradient.
• type
  character string "BFGS maximisation".
• constraints
  A list, describing the constrained optimization (NULL if unconstrained). Includes the following components:

  • type

  {type of constrained optimization} outer.iterations{number of iterations in the constraints step} barrier.value{value of the barrier function}

See Also

optim, nlm, maxNR, maxBHHH.

Examples

# Maximum Likelihood estimation of the parameter of Poissonian distribution
n <- rpois(100, 3)
loglik <- function(l) n*log(l) - l - lfactorial(n)
# we use numeric gradient
summary(maxBFGS(loglik, start=1))
# you would probably prefer mean(n) instead of that ;-)
# Note also that maxLik is better suited for Maximum Likelihood
###
### Now an example of constrained optimization
###
f <- function(theta) {
  x <- theta[1]
  y <- theta[2]
  exp(-(x^2 + y^2))
  ## Note: you may want to use exp(- theta \%*\% theta) instead ;-)
}
## use constraints: x + y >= 1
A <- matrix(c(1, 1), 1, 2)
B <- -1
res <- maxNM(f, start=c(1,1), constraints=list(ineqA=A, ineqB=B),
print.level=1)
print(summary(res))