title: Fitting 3d sigmoid to data
body: <p>I have data relating to a multivariant sigmoidal function: x y r(x,y) </p>
  
  <pre><code>x           y         r(x,y)
  
  0.468848997 0.487599    0
  0.468848997 0.512929    0
  0.468848997 0.538259    0
  0.468848997 0.563589    0
  0.468848997 0.588918    0
  0.468848997 0.614248    0
  0.468848997 0.639578    0
  0.468848997 0.664908    0.000216774
  0.468848997 0.690238    0.0235043
  0.468848997 0.715568    0.319768
  0.468848997 0.740897    0.855861
  0.468848997 0.766227    0.994637
  0.468848997 0.791557    0.999524
  0.468848997 0.816887    0.99954
  0.468848997 0.842217    0.99958
  0.468848997 0.867547    0.999572
  0.468848997 0.892876    0.999634
  0.468848997 0.918206    0.999566
  0.468848997 0.943536    0.999656
  0.468848997 0.968866    0.999637
  0.468848997 0.994196    0.999685
  .           .            .
  .           .            .
  .           .            .
  0.481520591 0.487599    0
  0.481520591 0.512929    0
  0.481520591 0.538259    0
  0.481520591 0.563589    0
  0.481520591 0.588918    0
  0.481520591 0.614248    0
  0.481520591 0.639578    1.09E-06
  0.481520591 0.664908    0.000755042
  0.481520591 0.690238    0.0498893
  0.481520591 0.715568    0.449531
  0.481520591 0.740897    0.919786
  0.481520591 0.766227    0.998182
  0.481520591 0.791557    0.99954
  </code></pre>
  
  <p>I wonder if there is a sigmoid function that I can use to fit my 3D data. 
  I came across this answer <a href="https://stackoverflow.com/questions/16509696/fitting-sigmoid-to-data">for 2D data</a> but I'm not able to extend it for my problem. </p>
  
  <p>I think in my guess the auxiliary function could look like this:</p>
  
  <pre><code>f(x,y)=1\(1+e^(-A0 x+A1))*( 1\(1+e^(-A2 y+A3)) with A0=A2 and A1=A3
  </code></pre>
  
  <p>I don't know how to proceed from here thought.</p>
  
  <p>I would be grateful for any insight or suggestion as I'm completely helpless now.</p>