mgwr.gwr.MGWR

class mgwr.gwr.MGWR(coords, y, X, selector, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, spherical=False, hat_matrix=False)[source]

Multiscale GWR estimation and inference.

Parameters
coordsarray-like

n*2, collection of n sets of (x,y) coordinates of observatons; also used as calibration locations is ‘points’ is set to None

yarray

n*1, dependent variable

Xarray

n*k, independent variable, exlcuding the constant

selectorsel_bw object

valid sel_bw object that has successfully called the “search” method. This parameter passes on information from GAM model estimation including optimal bandwidths.

familyfamily object

underlying probability model; provides distribution-specific calculations

sigma2_v1boolean

specify form of corrected denominator of sigma squared to use for model diagnostics; Acceptable options are:

‘True’: n-tr(S) (defualt) ‘False’: n-2(tr(S)+tr(S’S))

kernelstring

type of kernel function used to weight observations; available options: ‘gaussian’ ‘bisquare’ ‘exponential’

fixedboolean

True for distance based kernel function and False for adaptive (nearest neighbor) kernel function (default)

constantboolean

True to include intercept (default) in model and False to exclude intercept.

sphericalboolean

True for shperical coordinates (long-lat), False for projected coordinates (defalut).

hat_matrixboolean

True for computing and storing covariate-specific hat matrices R (n,n,k) and model hat matrix S (n,n). False (default) for computing MGWR inference on the fly.

Examples

#basic model calibration

>>> import libpysal as ps
>>> from mgwr.gwr import MGWR
>>> from mgwr.sel_bw import Sel_BW
>>> data = ps.io.open(ps.examples.get_path('GData_utm.csv'))
>>> coords = list(zip(data.by_col('X'), data.by_col('Y')))
>>> y = np.array(data.by_col('PctBach')).reshape((-1,1))
>>> rural = np.array(data.by_col('PctRural')).reshape((-1,1))
>>> fb = np.array(data.by_col('PctFB')).reshape((-1,1))
>>> african_amer = np.array(data.by_col('PctBlack')).reshape((-1,1))
>>> X = np.hstack([fb, african_amer, rural])
>>> X = (X - X.mean(axis=0)) / X.std(axis=0)
>>> y = (y - y.mean(axis=0)) / y.std(axis=0)
>>> selector = Sel_BW(coords, y, X, multi=True)
>>> selector.search(multi_bw_min=[2])
[92.0, 101.0, 136.0, 158.0]
>>> model = MGWR(coords, y, X, selector, fixed=False, kernel='bisquare', sigma2_v1=True)
>>> results = model.fit()
>>> print(results.params.shape)
(159, 4)
Attributes
coordsarray-like

n*2, collection of n sets of (x,y) coordinates of observatons; also used as calibration locations is ‘points’ is set to None

yarray

n*1, dependent variable

Xarray

n*k, independent variable, exlcuding the constant

selectorsel_bw object

valid sel_bw object that has successfully called the “search” method. This parameter passes on information from GAM model estimation including optimal bandwidths.

bwarray-like

collection of bandwidth values consisting of either a distance or N nearest neighbors; user specified or obtained using Sel_BW with fb=True. Order of values should the same as the order of columns associated with X

familyfamily object

underlying probability model; provides distribution-specific calculations

sigma2_v1boolean

specify form of corrected denominator of sigma squared to use for model diagnostics; Acceptable options are:

‘True’: n-tr(S) (defualt) ‘False’: n-2(tr(S)+tr(S’S))

kernelstring

type of kernel function used to weight observations; available options: ‘gaussian’ ‘bisquare’ ‘exponential’

fixedboolean

True for distance based kernel function and False for adaptive (nearest neighbor) kernel function (default)

constantboolean

True to include intercept (default) in model and False to exclude intercept.

sphericalboolean

True for shperical coordinates (long-lat), False for projected coordinates (defalut).

ninteger

number of observations

kinteger

number of independent variables

mean_yfloat

mean of y

std_yfloat

standard deviation of y

fit_paramsdict

parameters passed into fit method to define estimation routine

Warray-like

list of n*n arrays, spatial weights matrices for weighting all observations from each calibration point: one for each covariate (k)

Methods

fit(self[, n_chunks, pool])

Compute MGWR inference by chunk to reduce memory footprint.

predict(self)

Not implemented.

df_model

df_resid

__init__(self, coords, y, X, selector, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, spherical=False, hat_matrix=False)[source]

Initialize class