Two stage least squares with results and diagnostics.
Parameters: 
 y : array
nx1 array for dependent variable
 x : array
Two dimensional array with n rows and one column for each
independent (exogenous) variable, excluding the constant
 yend : array
Two dimensional array with n rows and one column for each
endogenous variable
 q : array
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)
 w : pysal W object
Spatial weights object (required if running spatial
diagnostics)
 robust : string
If ‘white’, then a White consistent estimator of the
variancecovariance matrix is given. If ‘hac’, then a
HAC consistent estimator of the variancecovariance
matrix is given. Default set to None.
 gwk : pysal W object
Kernel spatial weights needed for HAC estimation. Note:
matrix must have ones along the main diagonal.
 sig2n_k : boolean
If True, then use nk to estimate sigma^2. If False, use n.
 spat_diag : boolean
If True, then compute AnselinKelejian test (requires w)
 vm : boolean
If True, include variancecovariance matrix in summary
results
 name_y : string
Name of dependent variable for use in output
 name_x : list of strings
Names of independent variables for use in output
 name_yend : list of strings
Names of endogenous variables for use in output
 name_q : list of strings
Names of instruments for use in output
 name_w : string
Name of weights matrix for use in output
 name_gwk : string
Name of kernel weights matrix for use in output
 name_ds : string
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 pysal.lib
Open data on Columbus neighborhood crime (49 areas) using pysal.lib.io.open().
This is the DBF associated with the Columbus shapefile. Note that
pysal.lib.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 = pysal.lib.io.open(pysal.lib.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.
>>> 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: 
 summary : string
Summary of regression results and diagnostics (note: use in
conjunction with the print command)
 betas : array
kx1 array of estimated coefficients
 u : array
nx1 array of residuals
 predy : array
nx1 array of predicted y values
 n : integer
Number of observations
 k : integer
Number of variables for which coefficients are estimated
(including the constant)
 kstar : integer
Number of endogenous variables.
 y : array
nx1 array for dependent variable
 x : array
Two dimensional array with n rows and one column for each
independent (exogenous) variable, including the constant
 yend : array
Two dimensional array with n rows and one column for each
endogenous variable
 q : array
Two dimensional array with n rows and one column for each
external exogenous variable used as instruments
 z : array
nxk array of variables (combination of x and yend)
 h : array
nxl array of instruments (combination of x and q)
 robust : string
Adjustment for robust standard errors
 mean_y : float
Mean of dependent variable
 std_y : float
Standard deviation of dependent variable
 vm : array
Variance covariance matrix (kxk)
 pr2 : float
Pseudo R squared (squared correlation between y and ypred)
 utu : float
Sum of squared residuals
 sig2 : float
Sigma squared used in computations
 std_err : array
1xk array of standard errors of the betas
 z_stat : list of tuples
z statistic; each tuple contains the pair (statistic,
pvalue), where each is a float
 ak_test : tuple
AnselinKelejian test; tuple contains the pair (statistic,
pvalue)
 name_y : string
Name of dependent variable for use in output
 name_x : list of strings
Names of independent variables for use in output
 name_yend : list of strings
Names of endogenous variables for use in output
 name_z : list of strings
Names of exogenous and endogenous variables for use in
output
 name_q : list of strings
Names of external instruments
 name_h : list of strings
Names of all instruments used in ouput
 name_w : string
Name of weights matrix for use in output
 name_gwk : string
Name of kernel weights matrix for use in output
 name_ds : string
Name of dataset for use in output
 title : string
Name of the regression method used
 sig2n : float
Sigma squared (computed with n in the denominator)
 sig2n_k : float
Sigma squared (computed with nk in the denominator)
 hth : float
H’H
 hthi : float
(H’H)^1
 varb : array
(Z’H (H’H)^1 H’Z)^1
 zthhthi : array
Z’H(H’H)^1
 pfora1a2 : array
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
mean_y 

pfora1a2 

sig2n 

sig2n_k 

std_y 

utu 

vm 
