MultiStrauss            package:spatstat            R Documentation

_T_h_e _M_u_l_t_i_t_y_p_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 multitype Strauss point process model
     which can then be fitted to point pattern data.

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

       MultiStrauss(types, radii)

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

   types: Vector of all possible types (i.e. the possible levels of the
          'marks' variable in the data)

   radii: Matrix of interaction radii

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

     The (stationary) multitype Strauss process with m types, with
     interaction radii r[i,j] and  parameters beta[j] and gamma[i,j] is
     the pairwise interaction point process in which each point of type
     j contributes a factor beta[j] to the  probability density of the
     point pattern, and a pair of points of types i and j closer than
     r[i,j] units apart contributes a factor gamma[i,j] to the density.

     The nonstationary multitype Strauss process is similar except that
      the contribution of each individual point x[i] is a function
     beta(x[i]) of location and type, 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 multitype Strauss
     process pairwise interaction is yielded by the function
     'MultiStrauss()'. See the examples below.

     The matrix 'radii' must be symmetric, with entries which are
     either positive numbers or 'NA'.  A value of 'NA' indicates that
     no interaction term should be included for this combination of
     types.

     Note that only the interaction radii are specified in
     'MultiStrauss'. The canonical parameters log(beta[j]) and
     log(gamma[i,j]) 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 multitype Strauss process with
     interaction radii radii[i,j].

_W_a_r_n_i_n_g_s:

     The argument 'types' is interpreted as a set of factor levels.
     That is, in order that 'ppm' can fit the multitype Strauss model
     correctly to a point pattern 'X', this must be a marked point
     pattern; the mark vector 'X$marks' must be a factor; and  the
     argument 'types' must equal 'levels(X$marks)'.

_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', 'Strauss'

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

        r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
        MultiStrauss(1:2, r)
        # prints a sensible description of itself
        data(betacells)
        r <- 30.0 * matrix(c(1,2,2,1), nrow=2,ncol=2)
        ppm(betacells, ~1, MultiStrauss(c("off","on"), r), rbord=60.0)
        # fit the stationary multitype Strauss process to `betacells'
        ppm(betacells, ~polynom(x,y,3), MultiStrauss(c("off","on"), r), rbord=60.0)
        # fit a nonstationary Strauss process with log-cubic polynomial trend

