Multiple regression with betas constrained to be equal
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I would like to fit a multiple regression with beta constrained to be the same across variables.
Y = alpha + b1*X1 + b2*X2 +...+ b10*X10 where b1-b10 are equal, alpha unconstrained.
I have seen a number of examples where constraints are to keep beta in a certain range, but does not seem to be appropriate here.
2 Comments
Jon
on 27 Jul 2015
Can you not just follow one of the examples you cite but restrict the beta to be in a very tiny range?
John D'Errico
on 28 Jul 2015
Edited: John D'Errico
on 28 Jul 2015
Actually, trying to fix a variable by setting the bounds to a VERY narrow range tends to produce nastiness in the solution. It can cause problems. Anyway, this would not solve the problem as apparently asked, because the question was not to fix the b_i to a given value, but to make them all the same, while still estimating them.
Answers (1)
John D'Errico
on 28 Jul 2015
Edited: John D'Errico
on 28 Jul 2015
So you REALLY want to fit the model...
Y = alpha + b1*(X1 + X2 +...+ X10)
Hint. Hint. Hint. Does this look like a simple, linear regression in ONE variable? Could polyfit solve your problem?
2 Comments
John D'Errico
on 29 Jul 2015
:) Sometimes we just have a mental block, and need to view a problem from a different perspective.
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