Strauss               package:spatstat               R Documentation

_T_h_e _S_t_r_a_u_s_s _P_o_i_n_t _P_r_o_c_e_s_s _M_o_d_e_l

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

     Creates an instance of the Strauss point process model which can
     then be fitted to point pattern data.

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

       Strauss(r)

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

       r: The interaction radius of the Strauss process

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

     The (stationary) Strauss process with interaction radius r and 
     parameters beta and gamma is the pairwise interaction point
     process in which each point contributes a factor beta to the 
     probability density of the point pattern, and each pair of points
     closer than r units apart contributes a factor gamma to the
     density.

     Thus the probability density is

            f(x_1,...,x_n) = alpha . beta^n(x) gamma^s(x)

     where x[1],...,x[n] represent the  points of the pattern, n(x) is
     the number of points in the pattern, s(x) is the number of
     distinct unordered pairs of points that are closer than r units
     apart, and alpha is the normalising constant.

     The interaction parameter gamma must be less than or equal to 1 so
     that this model describes an ``ordered'' or ``inhibitive''
     pattern.

     The nonstationary Strauss process is similar except that  the
     contribution of each individual point x[i] is a function
     beta(x[i]) of location, rather than a constant beta. 

     The function 'ppm()', which fits point process models to  point
     pattern data, requires an argument  of class '"interact"'
     describing the interpoint interaction structure of the model to be
     fitted.  The appropriate description of the Strauss process
     pairwise interaction is yielded by the function 'Strauss()'. See
     the examples below.

     Note the only argument is the interaction radius 'r'. When 'r' is
     fixed, the model becomes an exponential family. The canonical
     parameters log(beta) and log(gamma) are estimated by 'ppm()', not
     fixed in 'Strauss()'.

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

     An object of class '"interact"' describing the interpoint
     interaction structure of the Strauss process with interaction
     radius r.

_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', 'pairwise.family', 'ppm.object'

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

        Strauss(r=0.1)
        # prints a sensible description of itself
        data(cells) 
        ppm(cells, ~1, Strauss(r=0.07), rbord=0.07)
        # fit the stationary Strauss process to `cells'
        ppm(cells, ~polynom(x,y,3), Strauss(r=0.07), rbord=0.1)
        # fit a nonstationary Strauss process with log-cubic polynomial trend

