R: Bootstrapping-based test for local spatial heteroscedasticity

LOSH.mc {spdep} | R Documentation

## 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.

### See Also

`LOSH`, `LOSH.mc`

### 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()"])

[Package spdep version 1.2-2 Index]