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 `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 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 `mpl()', 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 `mpl' 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:

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

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

        library(spatstat)
        r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
        MultiStrauss(1:2, r)
        # prints a sensible description of itself
        data(catWaessle)
        r <- 0.03 * matrix(c(1,2,2,1), nrow=2,ncol=2)
        mpl(catWaessle, ~1, MultiStrauss(c("0","1"), r), rbord=0.06)
        # fit the stationary multitype Strauss process to `catWaessle'
        mpl(catWaessle, ~polynom(x,y,3), MultiStrauss(c("0","1"), r), rbord=0.06)
        # fit a nonstationary Strauss process with log-cubic polynomial trend

