P-value from nlinfit

Hi

I'm using nlinfit to create an exponential fit in a correlation analysis. I would like to obtain the probability estimate of the model fit (or P-value). Can I find this in the covariance matrix? If so, in which index?

Best Morten

Answer 1

[Tom Lane]

For a function like

f = @(b,x) b(1) + b(2)*x.^b(3);

you might be interested in the p-value for a test of whether coefficients 2 and 3 could be zero. That tests whether this fit is significantly better than a horizontal (constant) line. Here's how you could do that:

[b,~,~,covb] = nlinfit(x,y,f,[1 1 1]);
p = linhyptest(b(2:3),covb(2:3,2:3));

There are other arguments you can supply to linhyptest to further specify the hypothesis. Also, it's more accurate to supply the dfe argument; what I did results in a normal rather than t test.

[Morten]

Perfect. Thanks.

However, in my case it would be even better to test the exponential fit (below) against a linear regression.

f = @(b,x)(b(1) + b(2)*exp(-b(3)*x))

Is that possible?

[Tom Lane]

There's not a formal way that I know about to do that test. The usual thing is to test two models where one is a special case of the other. In both your model and mine, the horizontal line is a special case of the three-parameter fit.

More informally, people do use AIC to compare models that are not nested one inside the other.