mgwr.gwr.MGWR¶

class mgwr.gwr.MGWR(coords, y, X, selector, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, dmat=None, sorted_dmat=None, spherical=False)[source]¶

Multiscale GWR estimation and inference.

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 selector : sel_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. family : family object underlying probability model; provides distribution-specific calculations 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 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:

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 selector : sel_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. bw : array-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 family : family object underlying probability model; provides distribution-specific calculations 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-like list of n*n arrays, spatial weights matrices for weighting all observations from each calibration point: one for each covariate (k)

Methods

fit()	Method that extracts information from Sel_BW (selector) object and prepares GAM estimation results for MGWRResults object.
predict()	Not implemented.

df_model
df_resid

__init__(coords, y, X, selector, sigma2_v1=True, kernel='bisquare', fixed=False, constant=True, dmat=None, sorted_dmat=None, spherical=False)[source]¶

Initialize class