R: Chi-square based test for local spatial heteroscedasticity

LOSH.cs {spdep} | R Documentation

## Chi-square based test for local spatial heteroscedasticity

### Description

The function implements the chi-square based test statistic for local spatial heteroscedasticity (LOSH) as proposed by Ord & Getis (2012).

### Usage

    LOSH.cs(x, listw, zero.policy = NULL, na.action = na.fail,
                     p.adjust.method = "none", 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`
`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.*)
`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.
`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

The test uses a = 2 (see `LOSH`) because chi-square based inference is not applicable with other exponents. The function makes use of `LOSH` in its calculations.

### 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 non-central Chi-square distribution with 2/Var.Hi degrees of freedom

### 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

`LOSH`, `LOSH.mc`

### Examples

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

[Package spdep version 1.2-2 Index]