syntax regression model variables

Hey! Can someone explain me the following syntax:

modelfun=@(b,x)b(1) + b(2)*x(:,1).^b(3)+... b(4)*x(:,2).^b(5); beta0=[-50 500 -1 500 -1]; mdl = fitnlm(ds,modelfun,beta0)

mdl = MPG~ b1 + b2*Horsepower^b3 + b4*Weight^b5

In particular I dont understand: (b,x)- this doesnt take any column of the dataset,right? x(:,1)- does this give me the first column of the dataset? x(:,1)-does this give me the second column of the dataset?

In beta0 I specify then the values of b1, b2 and b4? Or what is it for?

Thanks for your help!

Answer 1

[Roger Wohlwend]

The variable modelfun is a function handle and it defines the nonlinear model. Perhaps you should read the Matlab documentation about function handles first before you proceed with the regression. The first part of the handle - @(b,x) - tells matlab that the equation contains two variables: b (the coefficients) and x (the independent variables). Afterwards it shows the model.

Yes, x(:,1) is the first column of the matrix x.

beta0 specifys the inital values for the regression coefficients. Matlab needs them as a starting point for the optimization.

[Tania]

Thank you for your answer, helped a lot!Apart from fitnlm I saw there is also the command nlinfit, I dont really understand the difference.Do you know it? Also, how can I specify the values of beta0, I there a certain technique to specify them?And how do I decide on a equation? Do I have a look at the spread of the data & then choose a function I think is most appropriate? Thanks so much!

[Roger Wohlwend]

No, I don't know the difference between the two functions. Both seem appropriate for nonlinear regression, but I would prefer fitnlm.

There's a good technique to specify inital values. It's called gridsearch. Vary each coefficient in a certain range and find out which values yield the best model. Then use these values as inital values. In other words, calculate the model for different values for the coefficients and use that set of values as initial values that yielded the best model.

[Tania]

Thank you. I cant find gridsearch, is gridsearch the same as patternsearch?

[Roger Wohlwend]

No, gridsearch is probably not the same as patternsearch. You don't search for patterns. It is quite a simple concept. If you need a more detailed explanation, just ask.

[Tania]

Thanks, where can I find gridsearch in the documenation?Thanks!

[Roger Wohlwend]

It is not in the Matlab documentation. I found it in books.