spint.gravity.Doubly

class spint.gravity.Doubly(flows, origins, destinations, cost, cost_func, constant=True, framework='GLM', SF=None, CD=None, Lag=None, Quasi=False)

Doubly-constrained gravity-type spatial interaction model

Parameters

flowsarray of integers

n x 1; observed flows between O origins and D destinations

originsarray of strings

n x 1; unique identifiers of origins of n flows; when there are many origins it will be faster to use integers rather than strings for id labels.

destinationsarray of strings

n x 1; unique identifiers of destinations of n flows; when there are many destinations it will be faster to use integers rather than strings for id labels

costarray

n x 1; cost to overcome separation between each origin and destination associated with a flow; typically distance or time

cost_funcstring or function that has scalar input and output

functional form of the cost function; ‘exp’ | ‘pow’ | custom function

constantboolean

True to include intercept in model; True by default

yarray

n x 1; dependent variable used in estimation including any transformations

Xarray

n x k, design matrix used in estimation

frameworkstring

estimation technique; currently only ‘GLM’ is avaialble

Quasiboolean

True to estimate QuasiPoisson model; should result in same parameters as Poisson but with altered covariance; default to true which estimates Poisson model

SFarray

n x 1; eigenvector spatial filter to include in the model; default to None which does not include a filter; not yet implemented

CDarray

n x 1; competing destination term that accounts for the likelihood that alternative destinations are considered along with each destination under consideration for every OD pair; defaults to None which does not include a CD term; not yet implemented

LagW object

spatial weight for n observations (OD pairs) used to construct a spatial autoregressive model and estimator; defaults to None which does not include an autoregressive term; not yet implemented

Attributes

farray

n x 1; observed flows; dependent variable; y

ninteger

number of observations

kinteger

number of parameters

carray

n x 1; cost to overcome separation between each origin and destination associated with a flow; typically distance or time

cffunction

cost function; used to transform cost variable

oarray

n x 1; index of origin id’s

darray

n x 1; index of destination id’s

constantboolean

True to include intercept in model; True by default

paramsarray

n x k, estimated beta coefficients; k = # of origins + # of destinations; the first x-1 values pertain to the x destinations (leaving out the first destination to avoid perfect collinearity; no fixed effect), the next x values pertain to the x origins, and the final value is the distance decay coefficient

yhatarray

n x 1, predicted value of y (i.e., fittedvalues)

cov_paramsarray

Variance covariance matrix (kxk) of betas

std_errarray

k x 1, standard errors of betas

pvaluesarray

k x 1, two-tailed pvalues of parameters

tvaluesarray

k x 1, the tvalues of the standard errors

deviancefloat

value of the deviance function evalued at params; see family.py for distribution-specific deviance

resid_devarray

n x 1, residual deviance of model

llffloat

value of the loglikelihood function evalued at params; see family.py for distribution-specific loglikelihoods

llnullfloat

value of the loglikelihood function evaluated with only an intercept; see family.py for distribution-specific loglikelihoods

AICfloat

Akaike information criterion

D2float

percentage of explained deviance

adj_D2float

adjusted percentage of explained deviance

pseudo_R2float

McFadden’s pseudo R2 (coefficient of determination)

adj_pseudoR2float

adjusted McFadden’s pseudo R2

SRMSEfloat

standardized root mean square error

SSIfloat

Sorensen similarity index

resultsobject

Full results from estimated model. May contain addtional diagnostics

Example

——-

>>> import numpy as np

>>> import libpysal

>>> from spint.gravity import Doubly

>>> db = libpysal.io.open(libpysal.examples.get_path(‘nyc_bikes_ct.csv’))

>>> cost = np.array(db.by_col(‘tripduration’)).reshape((-1,1))

>>> flows = np.array(db.by_col(‘count’)).reshape((-1,1))

>>> d = np.array(db.by_col(‘d_tract’)).reshape((-1,1))

>>> o = np.array(db.by_col(‘o_tract’)).reshape((-1,1))

>>> model = Doubly(flows, o, d, cost, ‘exp’)

>>> model.params[-1:]

array([-0.00232112])

Methods

fit(self[, framework, Quasi])	Method that fits a particular count model usign the appropriate estimation technique.
local(self[, locs])	Not inmplemented for doubly-constrained models Not possible due to insufficient degrees of freedom.

SRMSE
SSI
reshape

__init__(self, flows, origins, destinations, cost, cost_func, constant=True, framework='GLM', SF=None, CD=None, Lag=None, Quasi=False)

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

Methods

SRMSE(self)
SSI(self)
__init__(self, flows, origins, destinations, …)	Initialize self.
fit(self[, framework, Quasi])	Method that fits a particular count model usign the appropriate estimation technique.
local(self[, locs])	Not inmplemented for doubly-constrained models Not possible due to insufficient degrees of freedom.
reshape(self, array)