spdep: LOSH.mc – R documentation

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LOSH.mc

Bootstrapping-based test for local spatial heteroscedasticity

Description

The function draws inferences about local spatial heteroscedasticity (LOSH) by means of the randomisation-based Monte-Carlo bootstrap proposed by Xu et al. (2014).

Usage

LOSH.mc(x, listw, a = 2, nsim = 99, zero.policy = NULL, na.action = na.fail, 
                    spChk = NULL, adjust.n = TRUE, p.adjust.method = "none")

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
`nsim`	the number of randomisations used in the bootstrap
`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()`
`adjust.n`	default TRUE, if FALSE the number of observations is not adjusted for no-neighbour observations, if TRUE, the number of observations is adjusted
`p.adjust.method`	a character string specifying the probability value adjustment for multiple tests, default "none"; see `p.adjustSP`. Note that the number of multiple tests for each region is only taken as the number of neighbours + 1 for each region, rather than the total number of regions.

Details

The test calculates LOSH (see LOSH) and estimates pseudo p-values from a conditional bootstrap. Thereby, the i-th value in each location is held fixed, whereas all other values are permuted nsim times over all other spatial units.

Value

`Hi`	LOSH statistic
`E.Hi`	expectation of LOSH
`Var.Hi`	variance of LOSH
`Z.Hi`	the approximately chi-square distributed test statistics
`x_bar_i`	local spatially weighted mean values
`ei`	residuals about local spatially weighted mean values
`Pr()`	p-values for `Hi` obtained from a conditional bootstrap distribution

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; Xu, M., Mei, C. L., & Yan, N. 2014. A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic. The Annals of Regional Science, 52 (3), 697–710.

Examples

data(columbus, package="spData")
    resLOSH_mc <- LOSH.mc(columbus$CRIME, nb2listw(col.gal.nb), 2, 100)
    resLOSH_cs <- LOSH.cs(columbus$CRIME, nb2listw(col.gal.nb))
    plot(resLOSH_mc[,"Pr()"], resLOSH_cs[,"Pr()"])

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