/*
**   maxlik10.e - Biochemical Oxygen Demand Model (decaying exponential)
**
**   The data are taken from Douglas M. Bates and Donald G. Watts,
**   Nonlinear Regression Analysis and Its Applications, page 270.
**
*/

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

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

z0 = {
     8.3 1,
    10.3 2,
    19.0 3,
    16.0 4,
    15.6 5,
    19.8 7 };

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


proc grd(b,z);
    local dev,s2,m,r;
    r = exp(-b[2]*z[.,2]);
    m = 1 - r;
    dev = z[.,1] - b[1]*m;
    s2 = dev'dev/rows(dev);
    dev = dev / s2;
    retp((dev.*m)~(b[1]*dev.*z0[.,2].* r));
endp;


start = { 20, .24 };

output file = maxlik10.out reset;

_max_GradProc = &grd;
_max_Options = { newton };

call maxprt(maxlik(z0,0,&lnlk,start));

output off;