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Re: Model fitting
Posted:
Nov 25, 2012 11:27 PM


On Nov 25, 2:03 am, Dmitry Zinoviev <dzinov...@gmail.com> wrote: > On Saturday, November 24, 2012 2:30:51 AM UTC5, Ray Koopman wrote: >> On Nov 23, 12:31 am, dzinov...@gmail.com wrote: >> >>> I have an array of 3D data in the form {xi,yi,0/1} (that is, the z coordinate is either 0 or 1). The points are not on a rectangular grid. The 0 and 1 areas are more or less contiguous, though the boundary between them can be somewhat fuzzy. The boundary is expected to be described by the equation y=a x^b. How can I adapt NonlinearModelFit or any other standard function to find the best fit values for a and b? Thanks! >> >> y = a x^b is linear in loglog coordinates, so use LogitModelFit >> with Log@x and Log@y as the predictors; i.e., the probability of >> observing z == 1 is 1/(1 + Exp[(b0 + b1*Log@x + b2*Log@y)]). > > Than you! I assume that b=b2/b1. How do I calculate a?
The boundary is the curve for which prob[z == 1] == 1/2:
Solve[1/(1 + Exp[(b0 + b1*Log@x + b2*Log@y)]) == 1/2, y]
y > E^(b0/b2) x^(b1/b2)



