reach                package:spatstat                R Documentation

_I_n_t_e_r_a_c_t_i_o_n _D_i_s_t_a_n_c_e _o_f _a _P_o_i_n_t _P_r_o_c_e_s_s

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

     Computes the interaction distance of a point process.

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

       reach(x, ...)
       reach.ppm(x, ..., epsilon=0)
       reach.interact(x, ...)

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

       x: Either a fitted point process model (object of class '"ppm"')
          or an interpoint interaction (object of class '"interact"'). 

 epsilon: Numerical threshold below which interaction is treated as
          zero. See details. 

     ...: Other arguments are ignored. 

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

     The `interaction distance' or `interaction range' of a point
     process model is the smallest distance D such that any two points
     in the process which are separated by a distance greater than D do
     not interact with each other.

     For example, the interaction range of a Strauss process (see
     'Strauss') with parameters beta,gamma,r is equal to r, unless
     gamma=1 in which case the model is Poisson and the interaction
     range is 0. The interaction range of a Poisson process is zero.
     The interaction range of the Ord threshold process (see
     'OrdThresh') is infinite, since two points _may_ interact at any
     distance apart.

     The function 'reach(x)' is generic, with methods for the case
     where 'x' is either

        *  a fitted point process model (object of class '"ppm"',
           usually obtained from the model-fitting function 'ppm');

        *  an interpoint interaction structure (object of class
           '"interact"'), created by one of the functions 'Poisson',
           'Strauss', 'StraussHard', 'MultiStrauss',
           'MultiStraussHard', 'Softcore', 'DiggleGratton', 'Pairwise',
           'PairPiece', 'Geyer', 'LennardJones', 'Saturated',
           'OrdThresh' or 'Ord'.

     When 'x' is an '"interact"' object, 'reach(x)' returns the maximum
     possible interaction range for any point process model with
     interaction structure given by 'x'. For example,
     'reach(Strauss(0.2))' returns '0.2'.

     When 'x' is a '"ppm"' object, 'reach(x)' returns the interaction
     range for the point process model represented by 'x'. For example,
     a fitted Strauss process model with parameters 'beta,gamma,r' will
     return either '0' or 'r', depending on whether the fitted
     interaction parameter 'gamma' is equal or not equal to 1.

     For some point process models, such as the soft core process (see
     'Softcore'), the interaction distance is infinite, because the
     interaction terms are positive for all pairs of points. A
     practical solution is to compute  the distance at which the
     interaction contribution from a pair of points falls below a
     threshold 'epsilon', on the scale of the log conditional
     intensity. This is done by setting the argument 'epsilon' to a
     positive value.

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

     The interaction distance, or 'NA' if this cannot be computed from
     the information given.

_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>

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

     'ppm', 'Poisson', 'Strauss', 'StraussHard', 'MultiStrauss',
     'MultiStraussHard', 'Softcore', 'DiggleGratton', 'Pairwise',
     'PairPiece', 'Geyer', 'LennardJones', 'Saturated', 'OrdThresh',
     'Ord'

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

         reach(Poisson())
         # returns 0

         reach(Strauss(r=7))
         # returns 7
         data(swedishpines)
         fit <- ppm(swedishpines, ~1, Strauss(r=7))
         reach(fit)
         # returns 7

         reach(OrdThresh(42))
         # returns Inf
         
         reach(MultiStrauss(1:2, matrix(c(1,3,3,1),2,2)))
         # returns 3

