pysal.model.spreg.
GM_Combo
(y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, 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 lag and 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 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.
>>> X = []
>>> X.append(db.by_col("INC"))
>>> X = np.array(X).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 create one
from columbus.shp
.
>>> w = pysal.lib.weights.Rook.from_shapefile(pysal.lib.examples.get_path("columbus.shp"))
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'
The Combo class runs an SARAR model, that is a spatial lag+error model. In this case we will run a simple version of that, where we have the spatial effects as well as exogenous variables. Since it is a spatial model, we have to pass in 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.
>>> reg = GM_Combo(y, X, w=w, name_y='crime', name_x=['income'], 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 spatial lag of the dependent variable. We can check the betas:
>>> print reg.name_z
['CONSTANT', 'income', 'W_crime', 'lambda']
>>> print np.around(np.hstack((reg.betas[:1],np.sqrt(reg.vm.diagonal()).reshape(3,1))),3)
[[ 39.059 11.86 ]
[ 1.404 0.391]
[ 0.467 0.2 ]]
And lambda:
>>> print 'lambda: ', np.around(reg.betas[1], 3)
lambda: [0.048]
This class also allows the user to run a spatial lag+error model with the extra feature of including nonspatial endogenous regressors. This means that, in addition to the spatial lag and error, we consider some of the variables on the righthand side of the equation as endogenous and we instrument for this. As an example, we will include HOVAL (home value) as endogenous and will instrument with DISCBD (distance to the CSB). We first need to read in the variables:
>>> yd = []
>>> yd.append(db.by_col("HOVAL"))
>>> yd = np.array(yd).T
>>> q = []
>>> q.append(db.by_col("DISCBD"))
>>> q = np.array(q).T
And then we can run and explore the model analogously to the previous combo:
>>> reg = GM_Combo(y, X, yd, q, w=w, name_x=['inc'], name_y='crime', name_yend=['hoval'], name_q=['discbd'], name_ds='columbus')
>>> print reg.name_z
['CONSTANT', 'inc', 'hoval', 'W_crime', 'lambda']
>>> names = np.array(reg.name_z).reshape(5,1)
>>> print np.hstack((names[0:4,:], np.around(np.hstack((reg.betas[:1], np.sqrt(reg.vm.diagonal()).reshape(4,1))),4)))
[['CONSTANT' '50.0944' '14.3593']
['inc' '0.2552' '0.5667']
['hoval' '0.6885' '0.3029']
['W_crime' '0.4375' '0.2314']]
>>> print 'lambda: ', np.around(reg.betas[1], 3)
lambda: [ 0.254]
Attributes: 


__init__
(y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, 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, w_lags, lag_q, …]) 
Initialize self. 
Attributes
mean_y 

std_y 