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 variancecovariance matrix is given. If ‘hac’, then a HAC consistent estimator of the variancecovariance 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 nk to estimate sigma^2. If False, use n.
 spat_diagboolean
If True, then compute AnselinKelejian test (requires w)
 vmboolean
If True, include variancecovariance 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 andpysal
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.
>>> 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
Adjustment for robust standard errors
 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, pvalue), where each is a float
 ak_testtuple
AnselinKelejian test; tuple contains the pair (statistic, pvalue)
 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 nk 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__
(self, 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__
(self, y, x, yend, q[, w, robust, …])Initialize self.
Attributes
mean_y
pfora1a2
sig2n
sig2n_k
std_y
utu
vm