esda.correlogram

esda.correlogram(geometry: ~geopandas.geoseries.GeoSeries, variable: str | list | ~pandas.core.series.Series | None, support: list | None = None, statistic: ~collections.abc.Callable | str = <class 'esda.moran.Moran'>, distance_type: str = 'band', weights_kwargs: dict = None, stat_kwargs: dict = None, select_numeric: bool = False, n_jobs: int = -1, n_bins: int | None = 50) → DataFrame

Generate a spatial correlogram

A spatial profile is a set of spatial autocorrelation statistics calculated for a set of increasing distances. It is a useful exploratory tool for examining how the relationship between spatial units changes over different notions of scale.

Parameters:

geometrygpd.GeoSeries

geodataframe holding spatial and attribute data

variable: pd.Series or list

pandas series matching input geometries

supportlist or None

list of values at which to compute the autocorrelation statistic

statisticcallable() or str

statistic to be computed for a range of libpysal.Graph specifications. This should be a class with a signature like Statistic(y,w, **kwargs) where y is a array and w is a libpysal.weights.W object Generally, this is a class from pysal’s esda package defaults to esda.Moran, which computes the Moran’s I statistic. If 'lowess' is provided, a non-parametric correlogram is computed using lowess regression on the spatial-covariation model, see Notes.

distance_typestr, optional

which concept of distance to increment. Options are {`band`, `knn`}. by default 'band' (for libpysal.weights.DistanceBand weights)

weights_kwargsdict

additional keyword arguments passed to the libpysal.weights.W class

stat_kwargsdict

additional keyword arguments passed to the esda autocorrelation statistic class. For example for faster results with no statistical inference, set the number of permutations to zero with stat_kwargs={permutations: 0}

select_numericbool

if True, only return numeric attributes from the original class. This is useful e.g. to prevent lists inside a “cell” of a dataframe

n_jobsint

number of jobs to pass to joblib. If -1 (default), all cores will be used

n_binsint

number of distance bands or k-nearest neighbor values to use if support is not provided. Ignored if support is provided. by default 10. If distance_type is ‘knn’, the number of neighbors will be capped at n-1, where n is the number of observations. Further, if n-1 is not divisible by n_bins, the actual number of bins will be may be off by one bin.

Returns:

outputspandas.DataFrame

table of autocorrelation statistics at increasing distance bandwidths

Notes

The nonparametric correlogram uses a lowess regression to estimate the spatial-covariation model:

\[zi*zj = f(d_{ij}) + e_ij\]

where \(f\) is a smooth function of distance \(d_{ij}\) between points \(i\) and \(j\). This function requires the statsmodels package to be installed.

For the nonparametric correlogram, a precomputed distance matrix can be used. To do this, set stat_kwargs={'metric':'precomputed', 'coordinates':distance_matrix} where distance_matrix is a square matrix of pairwise distances that aligns with the geometry rows.