mgwr.sel_bw.Sel_BW

class mgwr.sel_bw.Sel_BW(coords, y, X_loc, X_glob=None, family=<spglm.family.Gaussian object>, offset=None, kernel='bisquare', fixed=False, multi=False, constant=True, spherical=False)[source]

Select bandwidth for kernel

Methods: p211 - p213, bandwidth selection

[FBC02]: Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships.

Parameters
yarray

n*1, dependent variable.

X_globarray

n*k1, fixed independent variable.

X_locarray

n*k2, local independent variable, including constant.

coordslist of tuples

(x,y) of points used in bandwidth selection

familyfamily object/instance, optional

underlying probability model: Gaussian(), Poisson(), Binomial(). Default is Gaussian().

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

kernelstring, optional

kernel function: ‘gaussian’, ‘bisquare’, ‘exponential’. Default is ‘bisquare’.

fixedboolean

True for fixed bandwidth and False for adaptive (NN)

multiTrue for multiple (covaraite-specific) bandwidths

False for a traditional (same for all covariates) bandwdith; defualt is False.

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).

Examples

>>> import libpysal as ps
>>> 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))
>>> 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])

Golden section search AICc - adaptive bisquare

>>> bw = Sel_BW(coords, y, X).search(criterion='AICc')
>>> print(bw)
93.0

Golden section search AIC - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='AIC')
>>> print(bw)
50.0

Golden section search BIC - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='BIC')
>>> print(bw)
62.0

Golden section search CV - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='CV')
>>> print(bw)
68.0

Interval AICc - fixed bisquare

>>> sel = Sel_BW(coords, y, X, fixed=True)
>>> bw = sel.search(search_method='interval', bw_min=211001.0, bw_max=211035.0, interval=2)
>>> print(bw)
211025.0
Attributes
yarray

n*1, dependent variable.

X_globarray

n*k1, fixed independent variable.

X_locarray

n*k2, local independent variable, including constant.

coordslist of tuples

(x,y) of points used in bandwidth selection

familystring

GWR model type: ‘Gaussian’, ‘logistic, ‘Poisson’‘

kernelstring

type of kernel used and wether fixed or adaptive

fixedboolean

True for fixed bandwidth and False for adaptive (NN)

criterionstring

bw selection criterion: ‘AICc’, ‘AIC’, ‘BIC’, ‘CV’

search_methodstring

bw search method: ‘golden’, ‘interval’

bw_minfloat

min value used in bandwidth search

bw_maxfloat

max value used in bandwidth search

intervalfloat

interval increment used in interval search

tolfloat

tolerance used to determine convergence

max_iterinteger

max interations if no convergence to tol

multiTrue for multiple (covaraite-specific) bandwidths

False for a traditional (same for all covariates) bandwdith; defualt is False.

constantboolean

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

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

sphericalboolean

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

search_paramsdict

stores search arguments

int_scoreboolan

True if adaptive bandwidth is being used and bandwdith selection should be discrete. False if fixed bandwidth is being used and bandwidth does not have to be discrete.

bwscalar or array-like

Derived optimal bandwidth(s). Will be a scalar for GWR (multi=False) and a list of scalars for MGWR (multi=True) with one bandwidth for each covariate.

Sarray

n*n, hat matrix derived from the iterative backfitting algorthim for MGWR during bandwidth selection

Rarray

n*n*k, partial hat matrices derived from the iterative backfitting algoruthm for MGWR during bandwidth selection. There is one n*n matrix for each of the k covariates.

paramsarray

n*k, calibrated parameter estimates for MGWR based on the iterative backfitting algorithm - computed and saved here to avoid having to do it again in the MGWR object.

Methods

search(self[, search_method, criterion, …])

Method to select one unique bandwidth for a gwr model or a bandwidth vector for a mgwr model.

__init__(self, coords, y, X_loc, X_glob=None, family=<spglm.family.Gaussian object at 0x7f250214a048>, offset=None, kernel='bisquare', fixed=False, multi=False, constant=True, spherical=False)[source]

Initialize self. See help(type(self)) for accurate signature.