"NLREG.GPR: program to compute maximum likelihood estimates of
            nolinear least squares problem as a hint for Econ 551 midterm exam

            By John Rust, Yale University, March, 1997. ";

 /* STEP 1: Load in ASCII datasets and convert to GAUSS data sets
            with alternative-specific covariates for use in general
            form of multinomial logit model coded in EVAL.G.
	    Note the 3 coefficients (const, slope_a and slope_b) are
	    normalized to 0 for alternative 1. So estimate 3
	    coefficients for alternative 2.*/

   load dat[]=dat1.asc;
   dat=reshape(dat,rows(dat)/2,2);
   y=dat[.,1];  
   x=ones(rows(dat),1)~dat[.,2]~dat[.,2]^2~dat[.,2]^3;
   dat=y~x;
   dat=saved(dat,"dat1","vnames");
   let vnames=const b1 b2 b3 ; 

/* code to compute residuals  from first stage NLS regression
   to uncover  form of heteroscedasticity in second stage  */

/*    load beta;
   e=(y-exp(x*beta))^2;
   dat[.,1]=e;
   dat=saved(dat,"dat1","vnames"); */

   load gam;
   load beta; 

   iloc=seqa(2,1,4);
   cloc=0;
   dloc=1;
   q=zeros(4,1);
/*   q=beta; */
   infile="dat1";
   outfile="dat1.est";
   qsav="beta";
   dvar="y";
   let ivar=beta0 beta1 beta2 beta3;


/* Uncomment this line if you would like to run a derivative check,
   i.e. a comparison of numerical and analytical derivatives of the
   log-likelihood function  */

/*   call drvchk(dloc,iloc,cloc,q,infile,2000,outfile,qsav,&eval);  
     call hesschk(dloc,iloc,cloc,q,infile,2000,outfile,qsav,&eval); */

   /* Below is the main procedure that maximizes the likelihood function */

    call max(dvar,dloc,ivar,iloc,cloc,q,infile,500,outfile,qsav,&eval);