# logit.hessian: Hessian (curvature matrix) In Bhat: General likelihood exploration

## Description

Numerical evaluation of the Hessian of a real function f: R^n -> R on a generalized logit scale, i.e. using transformed parameters according to x'=log((x-xl)/(xu-x))), with xl < x < xu.

## Usage

 `1` ```logit.hessian(x=x, f=f, del=rep(0.002, length(x\$est)), dapprox=FALSE, 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 for which the Hessian is to be computed at point x `del` step size on logit scale (numeric) `dapprox` logical variable. If TRUE the off-diagonal elements are set to zero. If FALSE (default) the full Hessian is computed `nfcn` number of function calls

## Details

This version uses a symmetric grid for the numerical evaluation computation of first and second derivatives.

## Value

returns list with

 `df ` first derivatives (logit scale) `ddf ` Hessian (logit scale) `nfcn ` number of function calls `eigen ` eigen values (logit scale)

## Note

This function is part of the Bhat exploration tool

## Author(s)

E. Georg Luebeck (FHCRC)

`dfp`, `newton`, `ftrf`, `btrf`, `dqstep`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` ## Rosenbrock Banana function fr <- function(x) { x1 <- x x2 <- x 100 * (x2 - x1 * x1)^2 + (1 - x1)^2 } ## define x <- list(label=c("a","b"),est=c(1,1),low=c(-100,-100),upp=c(100,100)) logit.hessian(x,f=fr,del=dqstep(x,f=fr,sens=0.01)) ## shows the differences in curvature at the minimum of the Banana ## function along principal axis (in a logit-transformed coordinate system) ```