pysal.model.spreg.
GM_Endog_Error
(y, x, yend, q, w, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None)[source]¶GMM method for a spatial error model with endogenous variables, with results and diagnostics; based on Kelejian and Prucha (1998, 1999) [Kelejian1998] [Kelejian1999].
Parameters: 


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 pysal.lib
>>> import numpy as np
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.
>>> dbf = 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([dbf.by_col('CRIME')]).T
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.
>>> x = np.array([dbf.by_col('INC')]).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).
>>> yend = np.array([dbf.by_col('HOVAL')]).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 = np.array([dbf.by_col('DISCBD')]).T
Since we want to run a spatial error model, we need to specify the spatial
weights matrix that includes the spatial configuration of the observations
into the error component of the model. To do that, we can open an already
existing gal file or create a new one. In this case, we will use
columbus.gal
, which contains contiguity relationships between the
observations in the Columbus dataset we are using throughout this example.
Note that, in order to read the file, not only to open it, we need to
append ‘.read()’ at the end of the command.
>>> w = pysal.lib.io.open(pysal.lib.examples.get_path("columbus.gal"), 'r').read()
Unless there is a good reason not to do it, the weights have to be rowstandardized so every row of the matrix sums to one. Among other things, this allows to interpret the spatial lag of a variable as the average value of the neighboring observations. In PySAL, this can be easily performed in the following way:
>>> w.transform='r'
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), the instruments and the weights matrix. 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.
>>> model = GM_Endog_Error(y, x, yend, q, w=w, name_x=['inc'], name_y='crime', name_yend=['hoval'], name_q=['discbd'], name_ds='columbus')
Once we have run the model, we can explore a little bit the output. The regression object we have created has many attributes so take your time to discover them. Note that because we are running the classical GMM error model from 1998/99, the spatial parameter is obtained as a point estimate, so although you get a value for it (there are for coefficients under model.betas), you cannot perform inference on it (there are only three values in model.se_betas). Also, this regression uses a two stage least squares estimation method that accounts for the endogeneity created by the endogenous variables included.
>>> print model.name_z
['CONSTANT', 'inc', 'hoval', 'lambda']
>>> np.around(model.betas, decimals=4)
array([[ 82.573 ],
[ 0.581 ],
[ 1.4481],
[ 0.3499]])
>>> np.around(model.std_err, decimals=4)
array([ 16.1381, 1.3545, 0.7862])
Attributes: 


__init__
(y, x, yend, q, w, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_w=None, name_ds=None)[source]¶Initialize self. See help(type(self)) for accurate signature.
Methods
__init__ (y, x, yend, q, w[, vm, name_y, …]) 
Initialize self. 
Attributes
mean_y 

std_y 