Parsing a Model at Run Time
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: NLREG2 */
/* TITLE: Parsing a Model at Run Time */
/* PRODUCT: IML */
/* SYSTEM: ALL */
/* KEYS: MATRIX SUGI6 */
/* PROCS: IML */
/* DATA: */
/* */
/* SUPPORT: Rick Wicklin UPDATE: SEP2013 */
/* REF: Originally a full-screen editor by WMS */
/* */
/****************************************************************/
proc iml;
/* _FUN and _DER are text strings that define model and deriv */
/* _parm contains parm names */
/* _beta contains initial values for parameters */
/* _k is the number of parameters */
start nlinit;
_dep = "uspop"; /* dependent variable */
_fun = "a0*exp(a1*time)"; /* nonlinear regression model */
/* deriv w.r.t. parameters */
_der = {"exp(a1*time)", "time*a0*exp(a1*time)"};
_parm = {"a0", "a1"}; /* names of parameters */
_beta = {3.9, 0}; /* initial guess for parameters */
_k= nrow(_parm); /* number of parameters */
finish nlinit;
/* Generate the following modules at run time: */
/* NLFIT: evaluate the model. After RUN NLFIT: */
/* _y contains response, */
/* _p contains predictor after call */
/* _r contains residuals */
/* _sse contains sse */
/* NLDERIV: evaluate derivs w.r.t params. After RUN NLDERIV: */
/* _x contains jacobian */
start nlgen;
call change(_fun, '*', '#', 0); /* substitute '#' for '*' */
call change(_der, '*', '#', 0);
/* Write the NLFIT module at run time */
call queue('start nlfit;');
do i=1 to _k;
call queue(_parm[i], "=_beta[", char(i,2), "];");
end;
call queue("_y = ", _dep, ";",
"_p = ", _fun, ";",
"_r = _y - _p;",
"_sse = ssq(_r);",
"finish;" );
/* Write the NLDERIV function at run time */
call queue('start nlderiv; free _NULL_; _x = ');
do i=1 to _k;
call queue("(", _der[i], ")||");
end;
call queue("_NULL_; finish;");
call queue("resume;"); /* Pause to compile the functions */
pause *;
finish nlgen;
/* Gauss-Newton nonlinear regression with Hartley step-halving */
start nlest;
run nlfit; /* f, r, and sse for initial beta */
/* Gauss-Newton iterations to estimate parameters */
do _iter=1 to 30 until(_eps<1e-8);
run nlderiv; /* subroutine for derivatives */
_lastsse = _sse;
_xpxi=sweep(_x`*_x);
_delta = _xpxi*_x`*_r; /* correction vector */
_old = _beta; /* save previous parameters */
_beta = _beta + _delta; /* apply the correction */
run nlfit; /* compute residual */
_eps = abs((_lastsse-_sse)) / (_sse+1e-6);
/* Hartley subiterations */
do _subit=1 to 10 while(_sse>_lastsse);
_delta = _delta/2; /* halve the correction vector */
_beta = _old+_delta; /* apply the halved correction */
run nlfit; /* find sse et al */
end;
/* if no improvement after 10 halvings, exit iter loop */
if _subit>10 then _eps=0;
end;
/* display table of results */
if _iter < 30 then do; /* convergence */
_dfe = nrow(_y) - _k;
_mse = _sse/_dfe;
_std = sqrt(vecdiag(_xpxi)#_mse);
_t = _beta/_std;
_prob = 1 - cdf("F", _t#_t, 1, _dfe);
print _beta[label="Estimate"] _std[label="Std Error"]
_t[label="t Ratio"] _prob[format=pvalue6.];
print _iter[label="Iterations"] _lastsse[label="SSE"];
end;
else print "Convergence failed";
finish nlest;
/* main program: run nonlinear regression on data */
uspop = {3929, 5308, 7239, 9638, 12866, 17069, 23191, 31443, 39818,
50155, 62947, 75994, 91972, 105710, 122775, 131669, 151325,
179323, 203211}/1000; /* US population, in thousands */
year = do(1790,1970,10)`;
time = year - 1790;
run nlinit; /* define strings that define the regression model */
run nlgen; /* write modules that evaluate the model */
run nlest; /* compute param estimates, std errs, and p-values */
