pysal.model.mgwr.gwr.GWR

class pysal.model.mgwr.gwr.GWR(coords, y, X, bw, family=<pysal.model.spglm.family.Gaussian object>, offset=None, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, dmat=None, sorted_dmat=None, spherical=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:
coords : array-like

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

y : array

n*1, dependent variable

X : array

n*k, independent variable, exlcuding the constant

bw : scalar

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

family : family object

underlying probability model; provides distribution-specific calculations

offset : array

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_v1 : boolean

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))

kernel : string

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

fixed : boolean

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

constant : boolean

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

dmat : array

n*n, distance matrix between calibration locations used to compute weight matrix. Defaults to None and is primarily for avoiding duplicate computation during bandwidth selection.

sorted_dmat : array

n*n, sorted distance matrix between calibration locations used to compute weight matrix. Defaults to None and is primarily for avoiding duplicate computation during bandwidth selection.

spherical : boolean

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

Examples

#basic model calibration

>>> import pysal.lib 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:
coords : array-like

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

y : array

n*1, dependent variable

X : array

n*k, independent variable, exlcuding the constant

bw : scalar

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

family : family object

underlying probability model; provides distribution-specific calculations

offset : array

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_v1 : boolean

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))

kernel : string

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

fixed : boolean

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

constant : boolean

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

dmat : array

n*n, distance matrix between calibration locations used to compute weight matrix. Defaults to None and is primarily for avoiding duplicate computation during bandwidth selection.

sorted_dmat : array

n*n, sorted distance matrix between calibration locations used to compute weight matrix. Defaults to None and is primarily for avoiding duplicate computation during bandwidth selection.

spherical : boolean

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

n : integer

number of observations

k : integer

number of independent variables

mean_y : float

mean of y

std_y : float

standard deviation of y

fit_params : dict

parameters passed into fit method to define estimation routine

W : array

n*n, spatial weights matrix for weighting all observations from each calibration point

points : array-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

P : array

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

exog_scale : scalar

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

exog_resid : array-like

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

Methods

fit([ini_params, tol, max_iter, solve, …]) Method that fits a model with a particular estimation routine.
predict(points, P[, exog_scale, exog_resid, …]) Method that predicts values of the dependent variable at un-sampled locations
df_model  
df_resid  
__init__(coords, y, X, bw, family=<pysal.model.spglm.family.Gaussian object>, offset=None, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, dmat=None, sorted_dmat=None, spherical=False)[source]

Initialize class

Methods

__init__(coords, y, X, bw[, family, offset, …]) Initialize class
df_model()
df_resid()
fit([ini_params, tol, max_iter, solve, …]) Method that fits a model with a particular estimation routine.
predict(points, P[, exog_scale, exog_resid, …]) Method that predicts values of the dependent variable at un-sampled locations

Attributes

mean_y
std_y