localG                 package:spdep                 R Documentation

_G _a_n_d _G_s_t_a_r _l_o_c_a_l _s_p_a_t_i_a_l _s_t_a_t_i_s_t_i_c_s

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

     The local spatial statistic G is calculated for each zone based on
     the spatial weights object used. The value returned is a Z-value,
     and may be used as a diagnostic tool. High positive values
     indicate the posibility of a local cluster of high values of the
     variable being analysed, very low relative values a similar
     cluster of low values. For inference, a Bonferroni-type test is
     suggested in the references, where tables of critical values may
     be found (see also details below).

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

     localG(x, listw, zero.policy=FALSE, spChk=NULL)

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

       x: a numeric vector the same length as the neighbours list in
          listw

   listw: a 'listw' object created for example by 'nb2listw'

zero.policy: if TRUE assign zero to the lagged value of zones without
          neighbours, if FALSE assign NA

   spChk: should the data vector names be checked against the spatial
          objects for identity integrity, TRUE, or FALSE, default NULL
          to use 'get.spChkOption()'

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

     If the neighbours member of listw has a "self.included" attribute
     set to TRUE, the Gstar variant, including the self-weight w_{ii} >
     0, is calculated and returned.  The returned vector will have a
     "gstari" attribute set to TRUE.  Self-weights can be included by
     using the 'include.self' function in the spweights package before
     converting the neighbour list to a spatial weights list with
     'nb2listw' as shown below in the example.

     The critical values of the statistic under assumptions given in
     the references for the 95th percentile are for n=1: 1.645, n=50:
     3.083, n=100: 3.289, n=1000: 3.886.

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

     A vector of G or Gstar values, with attributes "gstari" set to
     TRUE or FALSE, "call" set to the function call, and class
     "localG".

_A_u_t_h_o_r(_s):

     Roger Bivand Roger.Bivand@nhh.no

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

     Ord, J. K. and Getis, A. 1995 Local spatial autocorrelation
     statistics: distributional issues and an application.
     _Geographical Analysis_, 27, 286-306; Getis, A. and Ord, J. K.
     1996 Local spatial statistics: an overview. In P. Longley and M.
     Batty (eds) _Spatial analysis: modelling in a GIS environment_
     (Cambridge: Geoinformation International), 261-277.

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

     data(getisord)
     xycoords <- cbind(xyz$x, xyz$y)
     nb30 <- dnearneigh(xycoords, 0, 30)
     G30 <- localG(xyz$val, nb2listw(nb30, style="B"))
     G30[length(xyz$val)-136]
     nb60 <- dnearneigh(xycoords, 0, 60)
     G60 <- localG(xyz$val, nb2listw(nb60, style="B"))
     G60[length(xyz$val)-136]
     nb90 <- dnearneigh(xycoords, 0, 90)
     G90 <- localG(xyz$val, nb2listw(nb90, style="B"))
     G90[length(xyz$val)-136]
     nb120 <- dnearneigh(xycoords, 0, 120)
     G120 <- localG(xyz$val, nb2listw(nb120, style="B"))
     G120[length(xyz$val)-136]
     nb150 <- dnearneigh(xycoords, 0, 150)
     G150 <- localG(xyz$val, nb2listw(nb150, style="B"))
     G150[length(xyz$val)-136]
     brks <- seq(-5,5,1)
     cm.col <- cm.colors(length(brks)-1)
     image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),
       breaks=brks, col=cm.col, asp=1)
     text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7)
     polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
     title(main=expression(paste("Values of the ", G[i], " statistic")))
     G30s <- localG(xyz$val, nb2listw(include.self(nb30),
      style="B"))
     cat("value according to Getis and Ord's eq. 14.2, p. 263 (1996)\n")
     G30s[length(xyz$val)-136]
     cat(paste("value given by Getis and Ord (1996), p. 267",
       "(division by n-1 rather than n \n in variance)\n"))
     G30s[length(xyz$val)-136] *
       (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /
       sqrt(var(xyz$val)))
     image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),
       breaks=brks, col=cm.col, asp=1)
     text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7)
     polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
     title(main=expression(paste("Values of the ", G[i]^"*", " statistic")))

