# spreg.ThreeSLS¶

class spreg.ThreeSLS(bigy, bigX, bigyend, bigq, regimes=None, nonspat_diag=True, name_bigy=None, name_bigX=None, name_bigyend=None, name_bigq=None, name_ds=None, name_regimes=None)[source]

User class for 3SLS estimation

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

bigqdictionary

with matrix of instruments by equation

regimeslist

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.

nonspat_diag: boolean

flag for non-spatial diagnostics, default = True.

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 equation. default = None, but should be specified. is done when sur_stackZ is used.

name_dsstring

name for the data set.

name_regimesstring

name of regime variable for use in the output.

Examples

First import libpysal to load the spatial analysis tools.

>>> import libpysal


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.

>>> db = libpysal.io.open(libpysal.examples.get_path("NAT.dbf"),'r')


The specification of the model to be estimated can be provided as lists. Each equation should be listed separately. In this example, 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 = pysal.spreg.sur_utils.sur_dictxy(db,y_var,x_var)
>>> bigyend,bigyendvars = pysal.spreg.sur_utils.sur_dictZ(db,yend_var)
>>> bigq,bigqvars = pysal.spreg.sur_utils.sur_dictZ(db,q_var)


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 = ThreeSLS(bigy,bigX,bigyend,bigq,name_bigy=bigyvars,name_bigX=bigXvars,name_bigyend=bigyendvars,name_bigq=bigqvars,name_ds="NAT")
>>> reg.b3SLS
{0: array([[ 6.92426353],
[ 1.42921826],
[ 0.00049435],
[ 3.5829275 ]]), 1: array([[ 7.62385875],
[ 1.65031181],
[-0.21682974],
[ 3.91250428]])}

>>> reg.tsls_inf
{0: array([[  0.23220853,  29.81916157,   0.        ],
[  0.10373417,  13.77770036,   0.        ],
[  0.03086193,   0.01601807,   0.98721998],
[  0.11131999,  32.18584124,   0.        ]]), 1: array([[  0.28739415,  26.52753638,   0.        ],
[  0.09597031,  17.19606554,   0.        ],
[  0.04089547,  -5.30204786,   0.00000011],
[  0.13586789,  28.79638723,   0.        ]])}

Attributes
bigydictionary

with y values

bigZdictionary

with matrix of exogenous and endogenous variables for each equation

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

bigEarray

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

surchowarray

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

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

name_regimesstring

name of regime variable for use in the output

__init__(self, bigy, bigX, bigyend, bigq, regimes=None, nonspat_diag=True, name_bigy=None, name_bigX=None, name_bigyend=None, name_bigq=None, name_ds=None, name_regimes=None)[source]

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

Methods

 __init__(self, bigy, bigX, bigyend, bigq[, …]) Initialize self.