mauri

05-12-2008, 06:48 AM

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

I tried this quickly using the JMSL NonlinearRegression (http://www.vni.com/products/imsl/jmsl/v50/manual/api/com/imsl/stat/NonlinearRegression.html) 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);

}

}

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

05-12-2008, 12:39 PM

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

mecej4

04-25-2015, 08:37 AM

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.

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