nonlinear regression results

[mauri]

Hi,
I have a set of datapoints which i am trying to fit to the function
y = A*log(B+x) + C*x + D*sqrt(x)
and I am trying to use IMSL NonLinearRegression to do so.
An example of the data points i am trying to fit is attached:
The results are
A = 6.470
B = 0.827
C=-0.494
D= 4.009
I tried to compare the results with those generated by another library and those generated by other curve fitting softwares and, while the values of B, C and D agree with those calculated by IMSL NonLinearRegression, the value of A calculated with all other methods is 2.810.
Could anyone explain why am I getting different results?
Thanks in advance
Mauri

[ed]

I tried this quickly using the JMSL NonlinearRegression class and get the 2.81 value for A.

Can you tell us which version and IMSL product you're using? If you follow the example below and still get a different result, we'd be happy to look into it but would probably need your example code.

The code and results are included below; the code is based off of Example 1 in the documentation.

OUTPUT:
The computed regression coefficients are:
2.8102886812924983
0.8274741334082188
-0.4943239962786323
4.009283745461694
The sums of squares for error is 0.12211509207486902

import com.imsl.stat.*;

public class ForumNLR {
    public static void main(String args[])
        throws NonlinearRegression.TooManyIteration***ception,
        NonlinearRegression.NegativeFreqException,
        NonlinearRegression.NegativeWeightException {
        NonlinearRegression.Function f = new NonlinearRegression.Function() {

            public boolean f(double theta[], int iobs, double frq[], double wt[], double e[]) {
                double xdata[] = {0.048,0.091,0.091,0.091,0.082,0.13,0.138,0.176,0.214,0.226,
                	0.269,0.294,0.327,0.371,0.417,0.454,0.493,0.558,0.606,0.656,0.701,0.765,
                	0.814,0.879,0.93,0.991,1.073,1.13,1.194,1.279};
                double ydata[] = {0.6,0.8,0.8,0.8,1,1.2,1.4,1.6,1.8,2,2.2,2.4,2.6,2.8,3,3.2,
                	3.4,3.6,3.8,4,4.2,4.4,4.6,4.8,5,5.2,5.4,5.6,5.8,6};
                boolean iend;
                int nobs = 30;

                if(iobs < nobs){
                    wt[0] = 1.0;
                    frq[0] = 1.0;
                    iend = true;
                    e[0] = ydata[iobs]
                    		- theta[0] * Math.log(theta[1] + xdata[iobs])
                    		- theta[2] * xdata[iobs]
                    		- theta[3] * Math.sqrt(xdata[iobs]);
                } else {
                    iend = false;
                }
                return iend;
            }
        };

        int nparm = 4;
        double theta[] = {1, 1, 1, 1};
        NonlinearRegression regression = new NonlinearRegression(nparm);
        regression.setGuess(theta);
        double coef[] = regression.solve(f);
        System.out.println("The computed regression coefficients are:");
        for (int i=0; i<coef.length; i++) {
			System.out.println("\t" + coef[i]);
		}
        double sse = regression.getSSE();
        System.out.println("The sums of squares for error is " + sse);
    }
}

[ed]

On a whim, I just re-ran this in Java and changed the "Math.log" method call to "Math.log10" and got the following results:

The computed regression coefficients are:
6.470818030994914
0.8274702917257918
-0.49431002457446555
4.009304579667014
The sums of squares for error is 0.12211509207523491

So I guess you need to make sure you're calling the same LOG function in every program. It's interesting that the other parameters do not change at all.

[mauri]

now that explains it! thanks for your help, Ed! Much appreciated

[mecej4]

It's interesting that the other parameters do not change at all.

Switching from natural to common logarithms is equivalent to scaling A by ln 10. The remaining fit coefficients (B, C and D) are not affected by this scaling, so there is no surprise here.