/*
**   maxlik9.e   Likelihood Profile and Profile t traces for a
**               nonlinear least squares problem
**
**   The data for this example have been created using nlls.sim.
*/

library maxlik,pgraph;
#include maxlik.ext;
#include pgraph.ext;
maxset;

@ -- procedure to compute log-likelihood -- @

proc lnlk(b,z);
    local dev,s2;
    dev = z[.,1] - (b[1] * exp(-b[2]*z[.,2]));
    s2 = dev'dev/rows(dev);
    retp(lnpdfn2(dev,s2));
endp;

proc grdlk(b,z);
    local d,s2,dev,r;
    d = exp(-b[2]*z[.,2]);
    dev = z[.,1] - b[1]*d;
    s2 = dev'dev/rows(dev);
    r = dev.*d/s2;
    retp(r~(-b[1]*z[.,2].*r));
endp;

proc hslk(b,z);
    local d,s2,dev,r, hss;
    d = exp(-b[2]*z[.,2]);
    dev = z[.,1] - b[1]*d;
    s2 = dev'dev/rows(dev);
    r = -z[.,2].*d.*(b[1].*d + dev);
    hss = -d.*d/s2~r~b[1].*z[.,2].*r;
    retp(xpnd(sumc(hss)));
endp;


startv = { 2, 1 };
output file = maxlik9.out reset;

_max_GradProc = &grdlk;
_max_HessProc = &hslk;
__output = 5;

call maxprofile("nlls",0,&lnlk,startv);

output off;