spdep: LOSH – R documentation

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LOSH

Local spatial heteroscedasticity

Description

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.

Usage

LOSH(x, listw, a=2, var_hi=TRUE, zero.policy=NULL, na.action=na.fail, spChk=NULL)

Arguments

`x`	a numeric vector of the same length as the neighbours list in listw
`listw`	a `listw` object created for example by `nb2listw`
`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 `na.fail`), can also be `na.omit` or `na.exclude` - in these cases the weights list will be subsetted to remove NAs in the data. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations. Note that only weights lists created without using the glist argument to `nb2listw` may be subsetted. If `na.pass` is used, zero is substituted for NA values in calculating the spatial lag. (Note that na.exclude will only work properly starting from R 1.9.0, na.omit and na.exclude assign the wrong classes in 1.8.*)
`spChk`	should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use `get.spChkOption()`

Details

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.

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.

Examples

data(boston, package="spData")
    resLOSH <- LOSH(boston.c$NOX, nb2listw(boston.soi))
    hist(resLOSH[,"Hi"])
    mean(resLOSH[,"Hi"])

spdep

Spatial Dependence: Weighting Schemes, Statistics

v1.1-11

GPL (>= 2)

Authors

Roger Bivand [cre, aut] (<https://orcid.org/0000-0003-2392-6140>), Micah Altman [ctb], Luc Anselin [ctb], Renato Assunção [ctb], Olaf Berke [ctb], Andrew Bernat [ctb], Guillaume Blanchet [ctb], Eric Blankmeyer [ctb], Marilia Carvalho [ctb], Bjarke Christensen [ctb], Yongwan Chun [ctb], Carsten Dormann [ctb], Stéphane Dray [ctb], Virgilio Gómez-Rubio [ctb], Martin Gubri [ctb], Rein Halbersma [ctb], Elias Krainski [ctb], Pierre Legendre [ctb], Nicholas Lewin-Koh [ctb], Angela Li [ctb], Hongfei Li [ctb], Jielai Ma [ctb], Abhirup Mallik [ctb, trl], Giovanni Millo [ctb], Werner Mueller [ctb], Hisaji Ono [ctb], Pedro Peres-Neto [ctb], Gianfranco Piras [ctb], Markus Reder [ctb], Jeff Sauer [ctb], Michael Tiefelsdorf [ctb], René Westerholt [ctb], Levi Wolf [ctb], Danlin Yu [ctb]

Initial release

2021-09-07