# spreg.TSLS¶

class spreg.TSLS(y, x, yend, q, w=None, robust=None, gwk=None, sig2n_k=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_gwk=None, name_ds=None)[source]

Two stage least squares with results and diagnostics.

Parameters
yarray

nx1 array for dependent variable

xarray

Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant

yendarray

Two dimensional array with n rows and one column for each endogenous variable

qarray

Two dimensional array with n rows and one column for each external exogenous variable to use as instruments (note: this should not contain any variables from x)

wpysal W object

Spatial weights object (required if running spatial diagnostics)

robuststring

If ‘white’, then a White consistent estimator of the variance-covariance matrix is given. If ‘hac’, then a HAC consistent estimator of the variance-covariance matrix is given. Default set to None.

gwkpysal W object

Kernel spatial weights needed for HAC estimation. Note: matrix must have ones along the main diagonal.

sig2n_kboolean

If True, then use n-k to estimate sigma^2. If False, use n.

spat_diagboolean

If True, then compute Anselin-Kelejian test (requires w)

vmboolean

If True, include variance-covariance matrix in summary results

name_ystring

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_yendlist of strings

Names of endogenous variables for use in output

name_qlist of strings

Names of instruments for use in output

name_wstring

Name of weights matrix for use in output

name_gwkstring

Name of kernel weights matrix for use in output

name_dsstring

Name of dataset for use in output

Examples

We first need to import the needed modules, namely numpy to convert the data we read into arrays that spreg understands and pysal to perform all the analysis.

>>> import numpy as np
>>> import libpysal


Open data on Columbus neighborhood crime (49 areas) using libpysal.io.open(). This is the DBF associated with the Columbus shapefile. Note that libpysal.io.open() also reads data in CSV format; since the actual class requires data to be passed in as numpy arrays, the user can read their data in using any method.

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


Extract the CRIME column (crime rates) from the DBF file and make it the dependent variable for the regression. Note that PySAL requires this to be an numpy array of shape (n, 1) as opposed to the also common shape of (n, ) that other packages accept.

>>> y = np.array(db.by_col("CRIME"))
>>> y = np.reshape(y, (49,1))


Extract INC (income) vector from the DBF to be used as independent variables in the regression. Note that PySAL requires this to be an nxj numpy array, where j is the number of independent variables (not including a constant). By default this model adds a vector of ones to the independent variables passed in, but this can be overridden by passing constant=False.

>>> X = []
>>> X.append(db.by_col("INC"))
>>> X = np.array(X).T


In this case we consider HOVAL (home value) is an endogenous regressor. We tell the model that this is so by passing it in a different parameter from the exogenous variables (x).

>>> yd = []
>>> yd.append(db.by_col("HOVAL"))
>>> yd = np.array(yd).T


Because we have endogenous variables, to obtain a correct estimate of the model, we need to instrument for HOVAL. We use DISCBD (distance to the CBD) for this and hence put it in the instruments parameter, ‘q’.

>>> q = []
>>> q.append(db.by_col("DISCBD"))
>>> q = np.array(q).T


We are all set with the preliminars, we are good to run the model. In this case, we will need the variables (exogenous and endogenous) and the instruments. If we want to have the names of the variables printed in the output summary, we will have to pass them in as well, although this is optional.

>>> from spreg import TSLS
>>> reg = TSLS(y, X, yd, q, name_x=['inc'], name_y='crime', name_yend=['hoval'], name_q=['discbd'], name_ds='columbus')
>>> print(reg.betas)
[[88.46579584]
[ 0.5200379 ]
[-1.58216593]]

Attributes
summarystring

Summary of regression results and diagnostics (note: use in conjunction with the print command)

betasarray

kx1 array of estimated coefficients

uarray

nx1 array of residuals

predyarray

nx1 array of predicted y values

ninteger

Number of observations

kinteger

Number of variables for which coefficients are estimated (including the constant)

kstarinteger

Number of endogenous variables.

yarray

nx1 array for dependent variable

xarray

Two dimensional array with n rows and one column for each independent (exogenous) variable, including the constant

yendarray

Two dimensional array with n rows and one column for each endogenous variable

qarray

Two dimensional array with n rows and one column for each external exogenous variable used as instruments

zarray

nxk array of variables (combination of x and yend)

harray

nxl array of instruments (combination of x and q)

robuststring

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

vmarray

Variance covariance matrix (kxk)

pr2float

Pseudo R squared (squared correlation between y and ypred)

utufloat

Sum of squared residuals

sig2float

Sigma squared used in computations

std_errarray

1xk array of standard errors of the betas

z_statlist of tuples

z statistic; each tuple contains the pair (statistic, p-value), where each is a float

ak_testtuple

Anselin-Kelejian test; tuple contains the pair (statistic, p-value)

name_ystring

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_yendlist of strings

Names of endogenous variables for use in output

name_zlist of strings

Names of exogenous and endogenous variables for use in output

name_qlist of strings

Names of external instruments

name_hlist of strings

Names of all instruments used in ouput

name_wstring

Name of weights matrix for use in output

name_gwkstring

Name of kernel weights matrix for use in output

name_dsstring

Name of dataset for use in output

titlestring

Name of the regression method used

sig2nfloat

Sigma squared (computed with n in the denominator)

sig2n_kfloat

Sigma squared (computed with n-k in the denominator)

hthfloat

$$H'H$$

hthifloat

$$(H'H)^{-1}$$

varbarray

$$(Z'H (H'H)^{-1} H'Z)^{-1}$$

zthhthiarray

$$Z'H(H'H)^{-1}$$

pfora1a2array

$$n(zthhthi)'varb$$

__init__(y, x, yend, q, w=None, robust=None, gwk=None, sig2n_k=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_gwk=None, name_ds=None)[source]

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

Methods

 __init__(y, x, yend, q[, w, robust, gwk, …]) Initialize self.

Attributes

property mean_y
property pfora1a2
property sig2n
property sig2n_k
property std_y
property utu
property vm