moranI               package:DCluster               R Documentation

_M_o_r_a_n'_s _I _a_u_t_o_c_o_r_r_e_l_a_t_i_o_n _s_t_a_t_i_s_t_i_c

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

     Moran's I statistic measures autocorrelation between areas within
     a region. It is similar to the correlation coefficient:


 I= n * [sum_i ( sum_j W_ij(Z_i-mean(Z))*(Z_j-mean(Z))]/[2 * (sum_i sum_j W_ij) * sum_k (Z_k-mean(Z))^2]


     W is a squared matrix which represents the relationship between
     each pair of regions. An usual approach is set w_ij to 1 if
     regions i and j have a common boundary and 0 otherwise, or it may
     represent the inverse distance between the centroids of these two
     regions.

     High values of this statistic may indicate the presence of groups
     of zones where values are unusually high. On the other hand, low
     values of the Moran's statistic will indicate no correlation
     between neighbouring areas, which may lead to indipendance in the
     observations. 

     _moranI.stat_ is the function to calculate the value of the
     statistic for residuals or SMRs of the data.

     _moranI.boot_ is used when performing a non-parametric bootstrap.

     _moranI.pboot_ is used when performing a parametric bootstrap.

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

     Moran, P. A. P. (1948). The interpretation os statistical maps.
     Journal of the Royal Statistical Society, Series B 10, 243-251.

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

     DCluster, moranI.stat, moranI.boot, moranI.pboot

