pysal.model.spreg.
GM_Lag
(y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, 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]¶Spatial two stage least squares (S2SLS) with results and diagnostics; Anselin (1988) [Anselin1988]
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. Since we will need some tests for our
model, we also import the diagnostics module.
>>> import numpy as np
>>> import pysal.lib
>>> import pysal.model.spreg.diagnostics as D
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 HOVAL column (home value) 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("HOVAL"))
>>> y = np.reshape(y, (49,1))
Extract INC (income) and CRIME (crime rates) vectors 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.append(db.by_col("CRIME"))
>>> 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'
This class runs a lag model, which means that includes the spatial lag of the dependent variable on the righthand side of the equation. 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. The default most basic model to be run would be:
>>> reg=GM_Lag(y, X, w=w, w_lags=2, name_x=['inc', 'crime'], name_y='hoval', name_ds='columbus')
>>> reg.betas
array([[ 45.30170561],
[ 0.62088862],
[ 0.48072345],
[ 0.02836221]])
Once the model is run, we can obtain the standard error of the coefficient estimates by calling the diagnostics module:
>>> D.se_betas(reg)
array([ 17.91278862, 0.52486082, 0.1822815 , 0.31740089])
But we can also run models that incorporates corrected standard errors
following the White procedure. For that, we will have to include the
optional parameter robust='white'
:
>>> reg=GM_Lag(y, X, w=w, w_lags=2, robust='white', name_x=['inc', 'crime'], name_y='hoval', name_ds='columbus')
>>> reg.betas
array([[ 45.30170561],
[ 0.62088862],
[ 0.48072345],
[ 0.02836221]])
And we can access the standard errors from the model object:
>>> reg.std_err
array([ 20.47077481, 0.50613931, 0.20138425, 0.38028295])
The class is flexible enough to accomodate a spatial lag model that, besides the spatial lag of the dependent variable, includes other nonspatial endogenous regressors. As an example, we will assume that CRIME is actually endogenous and we decide to instrument for it with DISCBD (distance to the CBD). We reload the X including INC only and define CRIME as endogenous and DISCBD as instrument:
>>> X = np.array(db.by_col("INC"))
>>> X = np.reshape(X, (49,1))
>>> yd = np.array(db.by_col("CRIME"))
>>> yd = np.reshape(yd, (49,1))
>>> q = np.array(db.by_col("DISCBD"))
>>> q = np.reshape(q, (49,1))
And we can run the model again:
>>> reg=GM_Lag(y, X, w=w, yend=yd, q=q, w_lags=2, name_x=['inc'], name_y='hoval', name_yend=['crime'], name_q=['discbd'], name_ds='columbus')
>>> reg.betas
array([[ 100.79359082],
[ 0.50215501],
[ 1.14881711],
[ 0.38235022]])
Once the model is run, we can obtain the standard error of the coefficient estimates by calling the diagnostics module:
>>> D.se_betas(reg)
array([ 53.0829123 , 1.02511494, 0.57589064, 0.59891744])
Attributes: 


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

pfora1a2 

sig2n 

sig2n_k 

std_y 

utu 

vm 