Description Usage Arguments Details Value Author(s) References See Also Examples

Local spatial heteroscedasticity is calculated for each location based on the spatial weights object used. The statistic is:

*H_i = \frac{∑_j^n w_{ij} \cdot |e_j|^a}{h_1 \cdot ∑_j^n w_{ij}}*

with

*e_j = x_j - \bar{x}_j*

and

*\bar{x}_j = \frac{∑_k^n w_{jk} \cdot x_k}{∑_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.

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`x` |
a numeric vector of the same length as the neighbours list in listw |

`listw` |
a |

`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, |

`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 |

`spChk` |
should the data vector names be checked against the spatial objects for identity integrity, TRUE, or FALSE, default NULL to use |

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 |

René Westerholt rene.westerholt@tu-dortmund.de

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

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