eem                 package:spatstat                 R Documentation

_E_x_p_o_n_e_n_t_i_a_l _E_n_e_r_g_y _M_a_r_k_s

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

     Given a point process model fitted to a point pattern, compute the
     Stoyan-Grabarnik diagnostic ``exponential energy marks'' for the
     data points.

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

       eem(fit)

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

     fit: The fitted point process model. An object of class '"ppm"'. 

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

     Stoyan and Grabarnik (1991) proposed a diagnostic tool for point
     process models fitted to spatial point pattern data. Each point
     x_i of the data pattern X is given a `mark' or `weight'

                   m_i = frac 1 {hatlambda(x_i,X)}

     where hatlambda(x_i,X) is the conditional intensity of the fitted
     model. If the fitted model is correct, then the sum of these marks
     for all points in a region B has expected value equal to the area
     of B.

     The argument 'fit' must be a fitted point process model (object of
     class '"ppm"'). Such objects are produced by the maximum
     pseudolikelihood fitting algorithm 'ppm'). This fitted model
     object contains complete information about the original data
     pattern and the model that was fitted to it.

     The value returned by 'eem' is the vector of weights m_i
     associated with the points x_i of the original data pattern. The
     original data pattern (in corresponding order) can be extracted
     from 'fit' using 'data.ppm'.

     The function 'diagnose.ppm' produces a set of sensible diagnostic
     plots based on these weights.

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

     A vector containing the values of the exponential energy mark for
     each point in the pattern.

_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>

_R_e_f_e_r_e_n_c_e_s:

     Stoyan, D. and Grabarnik, P. (1991) Second-order characteristics
     for stochastic structures connected with Gibbs point processes.
     _Mathematische Nachrichten_, 151:95-100.

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

     'diagnose.ppm', 'ppm.object', 'data.ppm', 'residuals.ppm', 'ppm'

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

         data(cells)
         fit <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
         ee <- eem(fit)
         sum(ee)/area.owin(cells$window) # should be about 1 if model is correct
         Y <- setmarks(cells, ee)
         plot(Y, main="Cells data\n Exponential energy marks")

