Constrained regression with constrains on the slopes
2 views (last 30 days)
Show older comments
I was the following regeression specification
ln Q = ln A + alpha * ln K + beta * ln L
I want to fins alpha and beta such that alpha + beta < 1 and alpha > 0 and beta > 0.
I am trying to use lsqlin but I don't understand how to write the specification.
5 Comments
Torsten
on 26 Jul 2022
But you want to fit Q against A*K^x(1)*L^x(2).
In the above code, you try to make A*K^x(1)*L^x(2) = 0.
Answers (1)
Matt J
on 26 Jul 2022
Edited: Matt J
on 26 Jul 2022
AA=log(K(:)./L(:));
bb=log(Q(:)./A(:)./L(:));
alpha=min( max(AA\bb,0) ,1 );
beta=1-alpha;
2 Comments
Matt J
on 27 Jul 2022
Edited: Matt J
on 27 Jul 2022
Darn it. Well then, why not with lsqlin as originally proposed,
C=[log(K(:)) log(L(:));
d=log(Q(:)./A(:));
x0=lsqlin(C,d,[1,1],1,[],[],[0 0],[1,1]);
alpha=x0(1);
beta=x0(2);
If desired, you can use x0 to initialize a a nonlinear least squares fit to the original non-logged model,
fun = @(x,KL) A(:).'*KL.^x;
lb = [0, 0];
ub = [1, 1];
x=lsqcurvefit(fun,x0(:)',[K(:),L(:)], Q(:), lb,ub);
alpha=x(1);
beta=x(2);
See Also
Categories
Find more on Linear Least Squares in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!