Fit model with 3 independent variables and many parameters to data?

Is it possible to use the fit() function to fit a model with 3 independent variables and many parameters (coefficients)? Reading through the documentation, I get the impression that Matlab only supports 2 independent variables. Any insight would be helpful.

Thanks, Justin

[Matt J]

For more general kinds of fitting, you probably need Optimization Toolbox solvers.

Answer 1

[Sean de Wolski]

Do you have the Statistics or Optimization Toolboxes? If so:

Optim:

* doc lsqcurvefit
* doc lsqlin
* doc lsqnonlin

Stats:

* doc NonlinearModel
* doc LinearModel
* doc regress

I'm missing many others, we can point you in a more specific direction if you have more details.

[Justin Solomon]

I do have those toolboxes so I think this gets me going in the right direction. Thanks! If you're curious, this is a really tricky fitting problem. I have a model that is a function of 3 independent variables (r, th, phi):

c=C*(1-(r/R(th,phi))^2)^n + cmin

Thus the parameters (or coefficients) I need to find are C, n, cmin, and R. The tricky part is that R is actually a function of th, and phi. This function is only numerically defined, i.e., I only need to know what R is at certain discrete values of th and phi. Therefore, I've been thinking of R as an array of parameters that I need to find. So if R is an m x n array, the total number of parameters I need to find is 3 + (m x n). In general, m and n will probably be somewhere between 5 and 20. This means that its possible that I have to do this fit with 3 independent variables and up to 403 parameters. Now that I've written this down, it seems kind of unreasonable. Any thoughts?

[Sean de Wolski]

Sorry, didn't read the last part about 403 parameters. That makes it sound less feasible. Can you post what you have.

[Justin Solomon]

Sorry, my code is a little bit messy right now (its written in a GUI and it would take me a while to put it in an understandable format).

I've implemented the lscurvefit() routine. It works in a reasonable amount of time if I give it a good starting guess and limits.

Anyways, is there a way to weight input data points (ydata)? In other words, some of my data points are less important than others so I would like to minimize a 'weighted' sum of square errors instead of the normal sum of square errors used by default. Possible? Thanks again for your help.

[Justin Solomon]

I just saw that I can use lsqnonlin() instead of lsqcurvefit() to do what I need because in lsqnonlin() the function that your minimizing is supposed to return the residuals instead of the predicted values as in lsqcurvefit(). Thus I can just weight the residuals that are returned in my function definition.

Answer 2

[Sander van Otterdijk]

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