MATLAB: Initial values in nlinfit or fitnlm

fitnlminitial valuesnlinfit

I am trying to run a non-linear multiple variable model in Matlab. The model has about 20 coefficients. I have been using 1s as my initial values in developing the model, and my model has an acceptable R2 value and good residual plots. However, I am not sure if the generated coefficients are sensitive to the initial values that were assigned by me.

This begs the question of whether one can check if the generated coefficient values are highly sensitive to the assigned initial values? Or one should do it manually, ie test the model with different set of initial values and compare the RMSE of the model?

Best Answer

A model with 20 parameters is likely going to be a challenge. If you have any doubts — and if you have the Global Optimization Toolbox — use the patternsearch (link) function to find the best parameter set. Another option is the genetic algorithm, the Global Optimization Toolbox ga (link) function.

I would also use the coefCI (link) function to determine if any of the confidence intervals for the coefficients (parameters) include zero, i.e. have opposite signs. If they do, they are not required for the model, since they are not statistically different from zero. This can help you ‘trim’ your model.

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MATLAB: Nlinfit to an equation

Your ‘GetValue’ function has a completely incorrect format!

See if this works:

function y = getValue(c,x) % where ci are the parameters
c1 = c(1);
c2 = c(2);
c3 = c(3);
A=0.5;
y = c1.*cos(x) + c2.*sin(x) + c3.*sin(2*x);
end

NOTE — This is UNTESTED CODE. It should work, but since I do not know what you are doing, and I do not have your data so I cannot test it, I cannot be certain it will work without modification.

MATLAB: Fit specific function on scatter plot Matlab

If y = exp(-beta*x) then log(y) = -beta*x and beta = -log(y)/x . Your best fit in log space would then be approximately

beta = mean( -log(y) ./ x )

In linear space,

beta = lsqcurvefit(@(beta,x) exp(-beta*x), 3, x, y);

However, when I constructed artificial data by defining beta and using

   c = 1;
   y = exp(-beta*x + randn(size(x)) * c );

and then fit against that to recover beta, then I found that a closer beta to the one I defined could be calculated as

other_beta = lsqcurvefit(@(beta,x) beta*x, 3, x, -log(y));

As c gets reduced to (say) 1/10 then the two fittings become more similar.

With a noise model like

c = 1/15;
y = exp(-beta*x) + (2 * rand(size(x)) - 1) * c;

then the original beta version becomes a notably better fit. So which one to use would probably depend upon the model of noise / error that you have.

Best Answer

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MATLAB: Fit specific function on scatter plot Matlab

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