spreg.GM_Combo_Het¶

class
spreg.
GM_Combo_Het
(y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, max_iter=1, epsilon=1e05, step1c=False, inv_method='power_exp', 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 heteroskedasticity and endogenous variables, with results and diagnostics; based on [ADKP10], following [Ans11].
 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 (always needed)
 w_lagsinteger
Orders of W to include as instruments for the spatially lagged dependent variable. For example, w_lags=1, then instruments are WX; if w_lags=2, then WX, WWX; and so on.
 lag_qboolean
If True, then include spatial lags of the additional instruments (q).
 max_iterint
Maximum number of iterations of steps 2a and 2b from [ADKP10]. Note: epsilon provides an additional stop condition.
 epsilonfloat
Minimum change in lambda required to stop iterations of steps 2a and 2b from [ADKP10]. Note: max_iter provides an additional stop condition.
 step1cboolean
If True, then include Step 1c from [ADKP10].
 inv_methodstring
If “power_exp”, then compute inverse using the power expansion. If “true_inv”, then compute the true inverse. Note that true_inv will fail for large n.
 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_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 HOVAL column (home values) 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) 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 class 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 = libpysal.weights.Rook.from_shapefile(libpysal.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, his 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_Het(y, X, w=w, step1c=True, name_y='hoval', 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. This class offers an error model that explicitly accounts for heteroskedasticity and that unlike the models from
spreg.error_sp
, it allows for inference on the spatial parameter. Hence, we find the same number of betas as of standard errors, which we calculate taking the square root of the diagonal of the variancecovariance matrix:>>> print reg.name_z ['CONSTANT', 'income', 'W_hoval', 'lambda'] >>> print np.around(np.hstack((reg.betas,np.sqrt(reg.vm.diagonal()).reshape(4,1))),4) [[ 9.9753 14.1435] [ 1.5742 0.374 ] [ 0.1535 0.3978] [ 0.2103 0.3924]]
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 CRIME (crime rates) 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("CRIME")) >>> 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_Het(y, X, yd, q, w=w, step1c=True, name_x=['inc'], name_y='hoval', name_yend=['crime'], name_q=['discbd'], name_ds='columbus') >>> print reg.name_z ['CONSTANT', 'inc', 'crime', 'W_hoval', 'lambda'] >>> print np.round(reg.betas,4) [[ 113.9129] [ 0.3482] [ 1.3566] [ 0.5766] [ 0.6561]]
 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
 e_filteredarray
nx1 array of spatially filtered residuals
 e_predarray
nx1 array of residuals (using reduced form)
 predyarray
nx1 array of predicted y values
 predy_earray
nx1 array of predicted y values (using reduced form)
 ninteger
Number of observations
 kinteger
Number of variables for which coefficients are estimated (including the constant)
 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)
 iter_stopstring
Stop criterion reached during iteration of steps 2a and 2b from [ADKP10].
 iterationinteger
Number of iterations of steps 2a and 2b from [ADKP10].
 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)
 pr2_efloat
Pseudo R squared (squared correlation between y and ypred_e (using reduced form))
 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
 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_dsstring
Name of dataset for use in output
 titlestring
Name of the regression method used
 hthfloat
\(H'H\)

__init__
(self, y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, max_iter=1, epsilon=1e05, step1c=False, inv_method='power_exp', 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__
(self, y, x[, yend, q, w, w_lags, …])Initialize self.
Attributes
mean_y
std_y