`LOSH.Rd`

Local spatial heteroscedasticity is calculated for each location based on the spatial weights object used. The statistic is:
$$H_i = \frac{\sum_j^n w_{ij} \cdot |e_j|^a}{h_1 \cdot \sum_j^n w_{ij}}$$ with $$e_j = x_j - \bar{x}_j$$ and $$\bar{x}_j = \frac{\sum_k^n w_{jk} \cdot x_k}{\sum_k^n w_{jk}}$$
Its expectation and variance are given in Ord & Getis (2012). The exponent *a* allows for investigating different types of mean dispersal.

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

- 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()`

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.

- 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

Ord, J. K., & Getis, A. 2012. Local spatial heteroscedasticity (LOSH), The Annals of Regional Science, 48 (2), 529--539.