localG | R Documentation |

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).

localG(x, listw, zero.policy=NULL, spChk=NULL, return_internals=FALSE, GeoDa=FALSE, alternative = "two.sided") localG_perm(x, listw, nsim=499, zero.policy=NULL, spChk=NULL, return_internals=TRUE, alternative = "two.sided", iseed=NULL)

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

`listw` |
a |

`zero.policy` |
default NULL, use global option value; 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 |

`return_internals` |
default FALSE but TRUE for permutation version, if TRUE, return internal values of G, EI and VG as as attribute matrix |

`GeoDa` |
default FALSE, if TRUE, drop x values for no-neighbour and self-neighbour only observations from all summations |

`nsim` |
default 499, number of conditonal permutation simulations |

`alternative` |
a character string specifying the alternative hypothesis, must be one of |

`iseed` |
default NULL, used to set the seed for possible parallel RNGs |

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 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.

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

Conditional permutations added for comparative purposes; permutations are over the whole data vector omitting the observation itself.

Roger Bivand Roger.Bivand@nhh.no

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; Bivand RS, Wong DWS 2018 Comparing implementations of global and local indicators of spatial association. TEST, 27(3), 716–748 doi: 10.1007/s11749-018-0599-x

data(getisord, package="spData") # spData 0.3.2 changes x, y, xyz object names to go_x, go_y, go_xyz to # avoid putting these objects into the global environment via lazy loading if (exists("go_xyz") && packageVersion("spData") >= "0.3.2") { xyz <- go_xyz x <- go_x y <- go_y } xycoords <- cbind(xyz$x, xyz$y) nb30 <- dnearneigh(xycoords, 0, 30) G30 <- localG(xyz$val, nb2listw(nb30, style="B")) G30[length(xyz$val)-136] set.seed(1) G30_sim <- localG_perm(xyz$val, nb2listw(nb30, style="B")) G30_sim[length(xyz$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")))

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