title: Number of dummy points in spatstat
body: <p>I'm fitting a inhomogeneous Poisson model to a spatial point pattern dataset with function <code>ppm</code> (<code>spatstat</code> package) that uses Berman-Turner quadrature approximation for estimating the parameters by MLE. 
  By default, for computational reasons, the dummy points are arranged in a rectangular grid and the quadrature weights are determined dividing the observation window into a grid of rectangular tiles (the number of tiles is equal to the number of dummy points). </p>
  
  <p>Considering a square window, the number of dummy points generated automatically is a piecewise constant function (I suppose) that depends only on the number of data points (and not on the dimension of the window); more precisely:</p>
  
  <pre><code>  number of   │  number of
   data points  │ dummy points
   (intervals)  │  generated
  ──────────────────────────────
      0 -  225  │ 1028
    226 -  400  │ 1604   (4*401)
    401 -  625  │ 2504   (4*626)
    626 -  900  │ 3604   (4*901)
    901 - 1225  │ 4904  (4*1226)
       etc.     │     etc.
  </code></pre>
  
  <p><strong>My questions</strong> </p>
  
  <ul>
  <li>Why was this function chosen by default in <code>spatstat</code>? Is it a kind of 'rule of thumb'?</li>
  <li>Besides, could you point me articles or papers in which different methods and functions are compared to choose positions and number of dummy points?</li>
  </ul>