pysal.model.spreg.ThreeSLS

class pysal.model.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:
bigy : dictionary with vector for dependent variable by equation
bigX : dictionary with matrix of explanatory variables by equation

(note, already includes constant term)

bigyend : dictionary with matrix of endogenous variables by equation
bigq : dictionary with matrix of instruments by equation
regimes : list

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_bigy : dictionary with name of dependent variable for each equation

default = None, but should be specified is done when sur_stackxy is used

name_bigX : dictionary with names of explanatory variables for each

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

name_bigyend : dictionary with names of endogenous variables for each

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

name_bigq : dictionary with names of instrumental variables for each

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

name_ds : string; name for the data set
name_regimes : string; name of regime variable for use in the output

Examples

First import pysal.lib to load the spatial analysis tools.

>>> import pysal.lib

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

>>> db = pysal.lib.io.open(pysal.lib.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.model.spreg.sur_utils.sur_dictxy(db,y_var,x_var)
>>> bigyend,bigyendvars = pysal.model.spreg.sur_utils.sur_dictZ(db,yend_var)
>>> bigq,bigqvars = pysal.model.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:
bigy : dictionary with y values
bigZ : dictionary with matrix of exogenous and endogenous variables

for each equation

bigZHZH : dictionary with matrix of cross products Zhat_r’Zhat_s
bigZHy : dictionary with matrix of cross products Zhat_r’y_end_s
n_eq : number of equations
n : number of observations in each cross-section
bigK : vector with number of explanatory variables (including constant,

exogenous and endogenous) for each equation

b2SLS : dictionary with 2SLS regression coefficients for each equation
tslsE : N x n_eq array with OLS residuals for each equation
b3SLS : dictionary with 3SLS regression coefficients for each equation
varb : variance-covariance matrix
sig : Sigma matrix of inter-equation error covariances
bigE : n by n_eq array of residuals
corr : inter-equation 3SLS error correlation matrix
tsls_inf : dictionary with standard error, asymptotic t and p-value,

one for each equation

surchow : list with tuples for Chow test on regression coefficients

each tuple contains test value, degrees of freedom, p-value

name_ds : string; name for the data set
name_bigy : dictionary with name of dependent variable for each equation
name_bigX : dictionary with names of explanatory variables for each

equation

name_bigyend : dictionary with names of endogenous variables for each

equation

name_bigq : dictionary with names of instrumental variables for each

equations

name_regimes : string; name of regime variable for use in the output
__init__(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__(bigy, bigX, bigyend, bigq[, …]) Initialize self.