envelope              package:spatstat              R Documentation

_S_i_m_u_l_a_t_i_o_n _e_n_v_e_l_o_p_e_s _o_f _s_u_m_m_a_r_y _f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Computes simulation envelopes of a summary function.

_U_s_a_g_e:

       envelope(Y, fun=Kest, nsim=99, nrank=1, verbose=TRUE, ...)

_A_r_g_u_m_e_n_t_s:

       Y: Either a point pattern (object of class '"ppp"') or a fitted
          point process model (object of class '"ppm"'). 

     fun: Function that computes the desired summary statistic for a
          point pattern.  

    nsim: Number of simulated point patterns to be generated when
          computing the envelopes. 

   nrank: Rank of the envelope value amongst the 'nsim' simulated
          values. A rank of 1 means that the minimum and maximum
          simulated values will be used. 

 verbose: Logical flag indicating whether to print progress reports
          during the simulations. 

     ...: Extra arguments passed to 'fun'. 

_D_e_t_a_i_l_s:

     Simulation envelopes can be used to assess the goodness-of-fit of
     a point process model to point pattern data. See the References.

     If 'Y' is a point pattern (an object of class '"ppp"') then this
     routine generates 'nsim' simulations of Complete Spatial
     Randomness (i.e. 'nsim' simulated point patterns each being a
     realisation of the uniform Poisson point process) with the same
     intensity as the pattern 'Y'.

     If 'Y' is a fitted point process model (an object of class
     '"ppm"') then this routine generates 'nsim' simulated realisations
     of that model.

     The summary statistic 'fun' is applied to each of these simulated
     patterns. Typically 'fun' is one of the functions 'Kest', 'Gest',
     'Fest', 'Jest' or 'pcf'. It can also be a home-made function; it
     should return an object of class '"fv"'.

     Upper and lower pointwise envelopes are computed pointwise (i.e.
     for each value of the distance argument r), by sorting the 'nsim'
     simulated values, and taking the 'm'-th lowest and 'm'-th highest
     values, where 'm = nrank'. For example if 'nrank=1', the upper and
     lower envelopes are the pointwise maximum and minimum of the
     simulated values.

     The significance level of the associated Monte Carlo test is
     'alpha = 2 * nrank/(1 + nsim)'. 

     The return value is an object of class '"fv"' containing the
     summary function for the data point pattern and the upper and
     lower simulation envelopes. It can be plotted using 'plot.fv'.

     Arguments can be passed to the function 'fun' through '...'. This
     makes it possible to select the edge correction used to calculate
     the summary statistic. See the Examples.

_V_a_l_u_e:

     An object of class '"fv"', see 'fv.object', which can be plotted
     directly using 'plot.fv'.

     Essentially a data frame containing columns 

       r: the vector of values of the argument r  at which the summary
          function 'fun' has been  estimated 

     obs: values of the summary function for the data point pattern 

      lo: lower envelope of simulations 

      hi: upper envelope of simulations 

_A_u_t_h_o_r(_s):

     Adrian Baddeley adrian@maths.uwa.edu.au <URL:
     http://www.maths.uwa.edu.au/~adrian/> and Rolf Turner
     rolf@math.unb.ca <URL: http://www.math.unb.ca/~rolf>

_R_e_f_e_r_e_n_c_e_s:

     Cressie, N.A.C. _Statistics for spatial data_. John Wiley and
     Sons, 1991.

     Diggle, P.J. _Statistical analysis of spatial point patterns_.
     Arnold, 2003.

     Ripley, B.D. _Statistical inference for spatial processes_.
     Cambridge University Press, 1988.

     Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point
     fields: methods of geometrical statistics. John Wiley and Sons.

_S_e_e _A_l_s_o:

     'fv.object', 'plot.fv', 'Kest', 'Gest', 'Fest', 'Jest', 'pcf',
     'ppp', 'ppm'

_E_x_a_m_p_l_e_s:

      X <- rpoispp(42)

      # Envelope of K function under CSR
      ## Not run: 
      plot(envelope(X))
      
     ## End(Not run)
      

      # Translation edge correction (this is also FASTER):
      ## Not run: 
      plot(envelope(X, correction="translate"))
      
     ## End(Not run)
      

      # Envelope of K function for simulations from model 
      data(cells)
      fit <- ppm(cells, ~1, Strauss(0.05))
      ## Not run: 
      plot(envelope(fit))
      
     ## End(Not run)
      

      # Envelope of G function under CSR
      ## Not run: 
      plot(envelope(X, Gest))
      
     ## End(Not run)
      
      

