LOSH | R Documentation |
Local spatial heteroscedasticity is calculated for each location based on the spatial weights object used. The statistic is:
H_i = \frac{∑_j^n w_{ij} \cdot |e_j|^a}{h_1 \cdot ∑_j^n w_{ij}}
with
e_j = x_j - \bar{x}_j
and
\bar{x}_j = \frac{∑_k^n w_{jk} \cdot x_k}{∑_k^n w_{jk}}
Its expectation and variance are given in Ord & Getis (2012). The exponent a allows for investigating different types of mean dispersal.
LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=NULL, na.action=na.fail, spChk=NULL)
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, \bar{x}_i and e_i are calculated |
zero.policy |
default NULL, use global option value; if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA |
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 |
In addition to the LOSH measure, the values returned include local spatially weighted mean values \bar{x}_i and local residuals e_i 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.
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 |
René Westerholt rene.westerholt@tu-dortmund.de
Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529–539.
LOSH.cs
, LOSH.mc
data(boston, package="spData") resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi)) hist(resLOSH[,"Hi"]) mean(resLOSH[,"Hi"])
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