Re: Model fitting
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- Subject: [mg128793] Re: Model fitting
- From: Ray Koopman <koopman at sfu.ca>
- Date: Sun, 25 Nov 2012 23:26:57 -0500 (EST)
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On Nov 25, 2:03 am, Dmitry Zinoviev <dzinov... at gmail.com> wrote:
> On Saturday, November 24, 2012 2:30:51 AM UTC-5, Ray Koopman wrote:
>> On Nov 23, 12:31 am, dzinov... at 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 log-log 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)