Estimation of parameters for a non-linear model

Hi everyone,

I have a model that relates the average reaction time and error rate from an experimental session, with two free parameters, a and b:

ER=1/(1+a*(lnRT)^b )

I'm a bit confused by the multitude of ways to do the estimation of a and b. What's the simplest/reliable way to do it?

Many thanks!

[Matt J]

Which way do you consider complicated?

[AwedBy Matlab]

for instance after reading the help of fminsearch..

Answer 1

[Jonathan LeSage]

If you're using MATLAB 2011b or newer, you likely have access to the Curve Fitting app. If you have this tool installed, you can open it by typing cftool. This tool allows you to import your data and then define a custom equation to fit. Once you've imported your data, you can select "Custon Equation" from the fit type menu and define you're own equation to fit. The cftool is probably the most straightforward method for fitting nonlinear curves to experimental data. Here is a link to an introduction to the product and an example.

• http://www.mathworks.com/products/curvefitting/
• http://www.mathworks.com/help/curvefit/interactive-curve-and-surface-fitting-.html

Another option is to use the lsqcurvefit function to perform a nonlinear least squares fit of your custom defined equation using your data. Here is an example of this function being used:

• http://www.mathworks.com/help/optim/ug/nonlinear-curve-fitting-with-lsqcurvefit.html

Hopefully this helps to get you started!

Answer 2

[AwedBy Matlab]

Thanks very much Jonathan.