spreg.SURlagIV

class spreg.SURlagIV(bigy, bigX, bigyend=None, bigq=None, w=None, regimes=None, vm=False, regime_lag_sep=False, w_lags=1, lag_q=True, nonspat_diag=True, spat_diag=False, name_bigy=None, name_bigX=None, name_bigyend=None, name_bigq=None, name_ds=None, name_w=None, name_regimes=None)

User class for spatial lag estimation using IV

Parameters

bigydictionary

with vector for dependent variable by equation

bigXdictionary

with matrix of explanatory variables by equation (note, already includes constant term)

bigyenddictionary

with matrix of endogenous variables by equation (optional)

bigqdictionary

with matrix of instruments by equation (optional)

wspatial weights object, required

vmboolean

listing of full variance-covariance matrix, default = False

w_lagsinteger

order of spatial lags for WX instruments, default = 1

lag_qboolean

flag to apply spatial lag to other instruments, default = True

nonspat_diagboolean

flag for non-spatial diagnostics, default = True

spat_diagboolean

flag for spatial diagnostics, default = False

name_bigydictionary

with name of dependent variable for each equation. default = None, but should be specified. is done when sur_stackxy is used.

name_bigXdictionary

with names of explanatory variables for each equation. default = None, but should be specified. is done when sur_stackxy is used.

name_bigyenddictionary

with names of endogenous variables for each equation. default = None, but should be specified. is done when sur_stackZ is used.

name_bigqdictionary

with names of instrumental variables for each equations. default = None, but should be specified. is done when sur_stackZ is used.

name_dsstring

name for the data set

name_wstring

name for the spatial weights

Examples

First import libpysal to load the spatial analysis tools.

>>> import libpysal
>>> from libpysal.examples import load_example
>>> from libpysal.weights import Queen
>>> import spreg
>>> np.set_printoptions(suppress=True) #prevent scientific format

Open data on NCOVR US County Homicides (3085 areas) using libpysal.io.open(). This is the DBF associated with the NAT shapefile. Note that libpysal.io.open() also reads data in CSV format.

>>> nat = load_example('Natregimes')
>>> db = libpysal.io.open(nat.get_path('natregimes.dbf'), 'r')

The specification of the model to be estimated can be provided as lists. Each equation should be listed separately. Although not required, in this example we will specify additional endogenous regressors. Equation 1 has HR80 as dependent variable, PS80 and UE80 as exogenous regressors, RD80 as endogenous regressor and FP79 as additional instrument. For equation 2, HR90 is the dependent variable, PS90 and UE90 the exogenous regressors, RD90 as endogenous regressor and FP99 as additional instrument

>>> y_var = ['HR80','HR90']
>>> x_var = [['PS80','UE80'],['PS90','UE90']]
>>> yend_var = [['RD80'],['RD90']]
>>> q_var = [['FP79'],['FP89']]

The SUR method requires data to be provided as dictionaries. PySAL provides two tools to create these dictionaries from the list of variables: sur_dictxy and sur_dictZ. The tool sur_dictxy can be used to create the dictionaries for Y and X, and sur_dictZ for endogenous variables (yend) and additional instruments (q).

>>> bigy,bigX,bigyvars,bigXvars = spreg.sur_dictxy(db,y_var,x_var)
>>> bigyend,bigyendvars = spreg.sur_dictZ(db,yend_var)
>>> bigq,bigqvars = spreg.sur_dictZ(db,q_var)

To run a spatial lag model, we need to specify the spatial weights matrix. To do that, we can open an already existing gal file or create a new one. In this example, we will create a new one from NAT.shp and transform it to row-standardized.

>>> w = Queen.from_shapefile(nat.get_path("natregimes.shp"))
>>> w.transform='r'

We can now run the regression and then have a summary of the output by typing: print(reg.summary)

Alternatively, we can just check the betas and standard errors, asymptotic t and p-value of the parameters:

>>> reg = spreg.SURlagIV(bigy,bigX,bigyend,bigq,w=w,name_bigy=bigyvars,name_bigX=bigXvars,name_bigyend=bigyendvars,name_bigq=bigqvars,name_ds="NAT",name_w="nat_queen")
>>> reg.b3SLS
{0: array([[ 6.95472387],
       [ 1.44044301],
       [-0.00771893],
       [ 3.65051153],
       [ 0.00362663]]), 1: array([[ 5.61101925],
       [ 1.38716801],
       [-0.15512029],
       [ 3.1884457 ],
       [ 0.25832185]])}

>>> reg.tsls_inf
{0: array([[ 0.49128435, 14.15620899,  0.        ],
       [ 0.11516292, 12.50787151,  0.        ],
       [ 0.03204088, -0.2409087 ,  0.80962588],
       [ 0.1876025 , 19.45875745,  0.        ],
       [ 0.05450628,  0.06653605,  0.94695106]]), 1: array([[ 0.44969956, 12.47726211,  0.        ],
       [ 0.10440241, 13.28674277,  0.        ],
       [ 0.04150243, -3.73761961,  0.00018577],
       [ 0.19133145, 16.66451427,  0.        ],
       [ 0.04394024,  5.87893596,  0.        ]])}

Attributes

wspatial weights object

bigydictionary

with y values

bigZdictionary

with matrix of exogenous and endogenous variables for each equation

bigyenddictionary

with matrix of endogenous variables for each equation; contains Wy only if no other endogenous specified

bigqdictionary

with matrix of instrumental variables for each equation; contains WX only if no other endogenous specified

bigZHZHdictionary

with matrix of cross products Zhat_r’Zhat_s

bigZHydictionary

with matrix of cross products Zhat_r’y_end_s

n_eqint

number of equations

nint

number of observations in each cross-section

bigKarray

vector with number of explanatory variables (including constant, exogenous and endogenous) for each equation

b2SLSdictionary

with 2SLS regression coefficients for each equation

tslsEarray

N x n_eq array with OLS residuals for each equation

b3SLSdictionary

with 3SLS regression coefficients for each equation

varbarray

variance-covariance matrix

sigarray

Sigma matrix of inter-equation error covariances

residsarray

n by n_eq array of residuals

corrarray

inter-equation 3SLS error correlation matrix

tsls_infdictionary

with standard error, asymptotic t and p-value, one for each equation

joinrhotuple

test on joint significance of spatial autoregressive coefficient. tuple with test statistic, degrees of freedom, p-value

surchowarray

list with tuples for Chow test on regression coefficients each tuple contains test value, degrees of freedom, p-value

name_wstring

name for the spatial weights

name_dsstring

name for the data set

name_bigydictionary

with name of dependent variable for each equation

name_bigXdictionary

with names of explanatory variables for each equation

name_bigyenddictionary

with names of endogenous variables for each equation

name_bigqdictionary

with names of instrumental variables for each equations

__init__(bigy, bigX, bigyend=None, bigq=None, w=None, regimes=None, vm=False, regime_lag_sep=False, w_lags=1, lag_q=True, nonspat_diag=True, spat_diag=False, name_bigy=None, name_bigX=None, name_bigyend=None, name_bigq=None, name_ds=None, name_w=None, name_regimes=None)

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

Methods

__init__(bigy, bigX[, bigyend, bigq, w, …])

Initialize self.