Nonlinear multiple regression in SAS

Question

I have a data set with variables y, x₁, and x₂. I want to find an equation that fits the model:

y = k₁*x₁^c₁ + k₂*x₂^c₂

by finding k₁, c₁, k₂, and c₂. How do I do this in SAS? Specifically if there is an easy way in SAS Enterprise Guide, that's preferable.

Answer 1

First, there is no WYSIWYG in EG that I know of to do this.

You can use a number of procedures, getting them to converge (PROC MODEL comes to mind as a likely candidate) is not easy. I used PROC OPTMODEL from SAS/OR in this example.

data test;
do i=1 to 1000;
x1 = rannor(123)*10 + 100;
x2 = rannor(123)*2 + 10;
y = 10*(x1**2) + -10*(X2**3) + rannor(123);
output;
end;
run;

proc optmodel;
num n=1000;
set<num> indx;
num y{indx}, x1{indx}, x2{indx};
read data test into indx=[_N_] y x1 x2;

var k1 init 1000, 
    k2 init 1000, 
    c1 init 1 ,
    c2 init 1 , 
    mean init 0;

min sse = sum{i in indx}( (y[i]-(k1*x1[i]**c1 + k2*x2[i]**c2))**2 );

solve with nlp / maxiter=1000 ms;
print k1 k2 c1 c2;
quit;

Produces:

                    The OPTMODEL Procedure

                       Solution Summary

          Solver                       Multistart NLP
          Algorithm                    Interior Point
          Objective Function                      sse
          Solution Status               Best Feasible
          Objective Value                976.35152997

          Number of Starts                        100
          Number of Sample Points                2560
          Number of Distinct Optima                78
          Random Seed Used                      18410
          Optimality Error               0.0049799881
          Infeasibility                             0


                     k1         k2    c1    c2

                 9.9999    -9.9993     2     3