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 `mpl()', 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 `mpl()', 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:

     `mpl', `pairwise.family', `ppm.object'

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

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

