Multiple linear regression with constraint

I need some help with a code. I need to run a multiple linear regression such that the sum of the coefficients = 1 and I would like to drop the intercept. I have 7 variables, so i need 7 seven coefficients.

Thanks !

Answer 1

[John D'Errico]

Use lsqlin, IF you have the optimization toolbox.

Thus, if X is your nx7 design matrix, and Y an nx1 column vector, then the call to lsqlin would look like this:

lb = zeros(1,7);
ub = ones(1,7);
Aeq = ones(1,7);
beq = 1;
coef = lsqlin(X,Y,[],[],Aeq,beq,lb,ub);

There is no need to use a tool like fmincon as Amit has suggested. That tool is designed for nonlinear problems, which this is not. See that fmincon needs a starting value, and it will be considerably less efficient.

If you lack the optimization toolbox, this can still be solved using lsqnonneg, although that would require a transformation of the problem. Anyway, I'd strongly recommend a copy of that TB if you will do any work of this sort in the future.

[abdoulaye thiam]

Hello, John, How can I make sure that all my coefficient stay positive while using the "lsqlin"?

Answer 2

[Amit]

If you have 7 coefficients and there is a constrain that sum of coefficients are 1. Then, isn't technically you need to find only 6 coefficients while the 7th will be 1 - sum(all 6 coefficients)?

You can rearrange your linear regression model to incorporate this constrain.

[Cam_cat]

All my coefficients need to be between 0 and 1, so the constraint of 1-sum(all 6) might not be sufficient.

[Amit]

That part you missed out in the question.

You can use fmincon which can handle such constrains. You'll need to write the objective function that you're minimizing like abs(Y-Y_model)

More details on fmincon: http://www.mathworks.com/help/optim/ug/fmincon.html

And on how to write constrains: http://www.mathworks.com/help/optim/ug/writing-constraints.html

[John D'Errico]

NO NO NO NO NO NO NO NO! You do NOT need fmincon!!!!!! LSQLIN will suffice and is the appropriate tool to solve a linear problem subject to such types of constraints.

[Amit]

Wow .. so many NOs. I agree LSQLIN would be better and easier.

I suggested FMINCON, because thats something I use more often than any other optimization. I never use linear regression. However, one thing I'd say that FMINCON can solve it too. Longer process but it will solve it. But thank you, I learnt something new today. Thats what I love about MATLAB Answers.

[John D'Errico]

Ok, I just saw No, No, Nanette. :)

The point is, fmincon is a nonlinear solver. It uses an essentially iterative scheme to search for the solution, part of which requires it to differentiate the function.

If you KNOW the problem is essentially a linear one, then use a tool designed to solve a linear problem, so lsqlin here. It has no need to do any differentiation, no need to perform searches of the type that fmincon uses.

Answer 3

[andrea capone]

I havee the same truble:

the code that i have wrote contain in input Y vector 36*1, and X matrix 36*8. I want to use this script:

%multivariate regression Y =data_2(:,1); X =data_3(:,1:8); lb = zeros(1,8); ub = ones(1,8); Aeq = ones(1,8); beq = 1; coef = lsqlin(X,Y,[],[],Aeq,beq,lb,ub);

The variables are eight.

I have this error:Warning: The trust-region-reflective algorithm can handle bound constraints only; using active-set algorithm instead. > In lsqlin (line 300)

[Torsten]

The message you receive is not an error, but an information for you that the solution method has automatically been switched to active-set algorithm.

Best wishes

Torsten.

[andrea capone]

But I don't recive any solution!

Answer 4

[ARUN BORGOHAIN]

Can someone help me with regARIMA; as I donot have it; but I've both regression(say polyfit: I may use) & ARIMA tools; how to get the same output as with regARIMA! The same example as given in the matlab website can be taken! Beta=2.5 & -0.6; yt=2.5x2-0.6x1+ut; & in ut I would like to apply arima modelling & also get the same output! (Presently I m doing these in excel with lots of lots of consecutive steps & in R just in 3 steps!) But how to do in matlab!

https://in.mathworks.com/help/econ/regarima-class.html

Mdl = regARIMA('Intercept',0,'Beta',[2.5; -0.6],... 'AR',{0.7, -0.3, 0.1},'MA',{0.5, 0.2},... 'Variance',1,'D',1)