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

```
LOSH.cs(x, listw, zero.policy = attr(listw, "zero.policy"), 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 `attr(listw, "zero.policy")`

as set when `listw`

was created, if attribute not set, 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

## 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.cs(boston.c$NOX, nb2listw(boston.soi))
hist(resLOSH[,"Hi"])
mean(resLOSH[,"Hi"])
#> [1] 0.9919329
```