Spatial statistics operators

`stats.getis_ord`#

Getis and Ord's Gi* of every cell (PySAL's esda.G_Local with star and row-standardised weights, to rounding): the share of the map's total around the cell, itself included, its z and p, and the hot and cold spots at 90, 95 and 99% confidence (as ArcGIS's Gi_Bin: 1 to 3 hot, -1 to -3 cold).

Input	Type	What it is
`map`required	map	the values (positive)

Output	Type	What it is
`g`	map	Gi*
`z`	map	its z
`p`	map	its one-sided p (of \|z\|)
`spots`	map	3, 2, 1 hot spots at 99, 95, 90%; -1 to -3 cold; 0 none

Setting	Type	What it is
`contiguity`	text	the neighbours: queen (default, 8) or rook (4)

`stats.idw`#

Inverse distance weighting of points onto a map, as R's gstat (idw, to rounding): every cell the mean of the points' values weighted by one over the distance to a power, with every point or the nearest; a point's value at its own place.

Input	Type	What it is
`points`required	vector	the points, their values in an attribute
`like`required	map	the map whose cells to fill (those with a value)

Output	Type	What it is
`map`	map	the values interpolated

Setting	Type	What it is
`field`	text	the attribute of the values (default the only number)
`power`	number	the distance's power (default 2)
`nmax`	integer	the nearest points used (default all)

`stats.kriging`#

Ordinary kriging of points onto a map, as R's gstat (krige, to rounding): every cell the best linear unbiased prediction from the points' values under a variogram model (from stats.variogram, or given), with every point or the nearest, and the prediction's variance.

Input	Type	What it is
`points`required	vector	the points, their values in an attribute
`like`required	map	the map whose cells to fill (those with a value)
`model`	any	the variogram model (stats.variogram's model)

Output	Type	What it is
`prediction`	map	the values predicted
`variance`	map	the prediction's variance

Setting	Type	What it is
`field`	text	the attribute of the values (default the only number)
`nmax`	integer	the nearest points used (default all)
`shape`	text	without a model input: spherical, exponential or gaussian
`psill`	number	without a model input: the partial sill
`range`	number	without a model input: the range
`nugget`	number	without a model input: the nugget (default 0)

`stats.lisa`#

The local Moran's I of every cell (Anselin's LISA; PySAL's esda.Moran_Local, to rounding): how much it and its neighbours are alike, its quadrant (1 high among high, 2 low among high, 3 low among low, 4 high among low), its z under randomisation, a pseudo p of conditional permutations (its neighbours drawn among the other cells), and the clusters: the quadrant of the cells of p below alpha.

Input	Type	What it is
`map`required	map	the values

Output	Type	What it is
`i`	map	the local Moran's I
`quadrant`	map	1 high-high, 2 low-high, 3 low-low, 4 high-low
`z`	map	its z under randomisation
`p`	map	the pseudo p of the permutations
`clusters`	map	the quadrant where p < alpha, 0 elsewhere

Setting	Type	What it is
`permutations`	integer	per cell (default 99; 0 none)
`alpha`	number	the significance of the clusters (default 0.05)
`seed`	integer	the seed of the permutations (default 1)
`contiguity`	text	the neighbours: queen (default, 8) or rook (4)

`stats.moran`#

The global Moran's I of a map (PySAL's esda.Moran, to rounding): how much neighbouring cells are alike, over the contiguity of the cells with a value (row-standardised weights); its expectation, variance, z and two-sided p under normality and under randomisation, and a pseudo p of random permutations of the values.

Input	Type	What it is
`map`required	map	the values

Output	Type	What it is
`table`	table	I, EI, VI_norm, z_norm, p_norm, VI_rand, z_rand, p_rand, p_sim, n

Setting	Type	What it is
`permutations`	integer	the random permutations (default 999; 0 none)
`seed`	integer	the seed of the permutations (default 1)
`contiguity`	text	the neighbours: queen (default, 8) or rook (4)

`stats.trend`#

The monotonic trend of every cell along a series of maps (pymannkendall's original_test, the same numbers): the Mann-Kendall test (S, its variance corrected for ties, z, the two-sided p, Kendall's tau, increasing or decreasing at alpha) and Sen's slope (the median of the slopes between every pair of dates, per step of the series) with its intercept; the missing values of a cell left out.

Input	Type	What it is
`maps`required	raster	the maps, a layer per date (a stack, a loop's series, rasters)

Output	Type	What it is
`slope`	map	Sen's slope, per step
`intercept`	map	its intercept, at the first step
`p`	map	the Mann-Kendall test's two-sided p
`z`	map	its z
`tau`	map	Kendall's tau
`trend`	map	1 increasing, -1 decreasing, 0 none (at alpha)

Setting	Type	What it is
`alpha`	number	the significance level (default 0.05)

`stats.variogram`#

The sample variogram of points and a model fitted to it, as R's gstat (variogram and fit.variogram, to rounding): half the mean squared difference of the pairs of points in classes of distance up to a cutoff; a nugget and a spherical, exponential or Gaussian structure fitted by weighted least squares (the pairs over the squared distance as weights; a negative sill fixed at zero), for stats.kriging.

Input	Type	What it is
`points`required	vector	the points, their values in an attribute

Output	Type	What it is
`table`	table	a row per class with pairs: np, dist, gamma, model
`model`	any	the model fitted: {model, nugget, psill, range}

Setting	Type	What it is
`field`	text	the attribute of the values (default the only number)
`cutoff`	number	the largest distance (default a third of the diagonal)
`width`	number	the classes' width (default the cutoff / 15)
`model`	text	the structure: spherical (default), exponential, gaussian, none
`psill`	number	the partial sill to start from (default the variance)
`range`	number	the range to start from (default the cutoff / 3)
`nugget`	number	the nugget to start from (default the variance / 10)
`fit_nugget`	bool	fit the nugget (default true), else keep it

stats.getis_ord#

stats.idw#

stats.kriging#

stats.lisa#

stats.moran#

stats.trend#

stats.variogram#