mgwr.gwr.GWR

class mgwr.gwr.GWR(coords, y, X, bw, family=<spglm.family.Gaussian object>, offset=None, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, spherical=False, hat_matrix=False)[source]

Geographically weighted regression. Can currently estimate Gaussian, Poisson, and logistic models(built on a GLM framework). GWR object prepares model input. Fit method performs estimation and returns a GWRResults object.

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

bwscalar

bandwidth value consisting of either a distance or N nearest neighbors; user specified or obtained using Sel_BW

familyfamily object

underlying probability model; provides distribution-specific calculations

offsetarray

n*1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations; only for Poisson models

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 to store full n by n hat matrix, False to not store full hat matrix to minimize memory footprint (defalut).

Examples

#basic model calibration

>>> import libpysal as ps
>>> from mgwr.gwr import GWR
>>> 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))
>>> pov = np.array(data.by_col('PctPov')).reshape((-1,1))
>>> african_amer = np.array(data.by_col('PctBlack')).reshape((-1,1))
>>> X = np.hstack([rural, pov, african_amer])
>>> model = GWR(coords, y, X, bw=90.000, fixed=False, kernel='bisquare')
>>> results = model.fit()
>>> print(results.params.shape)
(159, 4)

#predict at unsampled locations

>>> index = np.arange(len(y))
>>> test = index[-10:]
>>> X_test = X[test]
>>> coords_test = np.array(coords)[test]
>>> model = GWR(coords, y, X, bw=94, fixed=False, kernel='bisquare')
>>> results = model.predict(coords_test, X_test)
>>> print(results.params.shape)
(10, 4)
Attributes
coordsarray-like

n*2, collection of n sets of (x,y) coordinates used for calibration locations

yarray

n*1, dependent variable

Xarray

n*k, independent variable, exlcuding the constant

bwscalar

bandwidth value consisting of either a distance or N nearest neighbors; user specified or obtained using Sel_BW

familyfamily object

underlying probability model; provides distribution-specific calculations

offsetarray

n*1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations

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 to store full n by n hat matrix, False to not store full hat matrix to minimize memory footprint (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

pointsarray-like

n*2, collection of n sets of (x,y) coordinates used for calibration locations instead of all observations; defaults to None unles specified in predict method

Parray

n*k, independent variables used to make prediction; exlcuding the constant; default to None unless specified in predict method

exog_scalescalar

estimated scale using sampled locations; defualt is None unless specified in predict method

exog_residarray-like

estimated residuals using sampled locations; defualt is None unless specified in predict method

Methods

fit(self[, ini_params, tol, max_iter, …])

Method that fits a model with a particular estimation routine.

predict(self, points, P[, exog_scale, …])

Method that predicts values of the dependent variable at un-sampled locations

df_model

df_resid

__init__(self, coords, y, X, bw, family=<spglm.family.Gaussian object at 0x7f251e016a58>, offset=None, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, spherical=False, hat_matrix=False)[source]

Initialize class