LOSH {spdep} | R Documentation |
Local spatial heteroscedasticity
Description
Local spatial heteroscedasticity is calculated for each location based on the spatial weights object used. The statistic is:
with
and
Its expectation and variance are given in Ord & Getis (2012). The exponent a allows for investigating different types of mean dispersal.
Usage
LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=attr(listw, "zero.policy"),
na.action=na.fail, spChk=NULL)
Arguments
x |
a numeric vector of the same length as the neighbours list in listw |
listw |
a |
a |
the exponent applied to the local residuals; the default value of 2 leads to a measure of heterogeneity in the spatial variance |
var_hi |
default TRUE, the moments and the test statistics are calculated for each location; if FALSE, only the plain LOSH measures, |
zero.policy |
default |
na.action |
a function (default |
spChk |
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use |
Details
In addition to the LOSH measure, the values returned include local spatially weighted mean values and local residuals
estimated about these means. These values facilitate the interpretation of LOSH values. Further, if specified through
var_hi
, the statistical moments and the test statistics as proposed by Ord & Getis (2012) are also calculated and returned.
Value
Hi |
LOSH statistic |
E.Hi |
(optional) expectation of LOSH |
Var.Hi |
(optional) variance of LOSH |
Z.Hi |
(optional) the approximately Chi-square distributed test statistics |
x_bar_i |
local spatially weighted mean values |
ei |
residuals about local spatially weighted mean values |
Author(s)
René Westerholt rene.westerholt@tu-dortmund.de
References
Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529–539.
See Also
Examples
data(boston, package="spData")
resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi))
hist(resLOSH[,"Hi"])
mean(resLOSH[,"Hi"])