kullnagar              package:DCluster              R Documentation

_K_u_l_l_d_o_r_f_f _a_n_d _N_a_g_a_r_w_a_l_l_a'_s _s_t_a_t_i_s_t_i_c _f_o_r _s_p_a_t_i_a_l _c_l_u_s_t_e_r_i_n_g.

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

     This method is based on creating a grid over the study area. Each
     point of the grid is taken to be the centre of all circles that
     contain up to a fraction of the total population. This is
     calculated by suming all the population of the regions whose
     centroids fall inside the circle. For each one of these balls, the
     likelihood ratio of the next test hypotheses is computed:

       H_0  :  p=q
       H_1  :  p>q

     where _p_ is the probability of being a case inside the ball and
     _q_ the probability of being a case outside it. Then, the ball
     where the maximum of the likelihood ratio is achieved is selected
     and its value is tested to assess whether it is significant or
     not.

     There are two possible statistics, depending on the model assumed
     for the data, which can be Bernouilli or Poisson. The value of the
     likelihood ratio  statistic is


                           max_z[L(z)/L_0]


     where _Z_ is the set of ball at a given point, _z_ an element of
     this set, L_0 is the likelihood under the null hypotheses and L(z)
     is the likelihood under the alternative hypotheses. The actual
     formulae involved in the calculation can be found in the reference
     given below.

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

     Kulldorff, Martin and Nagarwalla, Neville (1995). Spatial Disease
     Clusters: Detection and Inference. Statistics in Medicine 14,
     799-810.

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

     DCluster, kullnagar.stat, kullnagar.boot, kullnagar.pboot

