spreg.GM_Error_Het

class spreg.GM_Error_Het(y, x, w, max_iter=1, epsilon=1e-05, step1c=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None)

GMM method for a spatial error model with heteroskedasticity, 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

wpysal W object

Spatial weights object

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].

vmboolean

If True, include variance-covariance 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_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 and pysal 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) and CRIME (crime) 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 class adds a vector of ones to the independent variables passed in.

>>> 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 = 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 row-standardized 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'

We are all set with the preliminaries, we are good to run the model. In this case, we will need the variables 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.

>>> reg = GM_Error_Het(y, X, w=w, step1c=True, name_y='home value', name_x=['income', 'crime'], 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.

>>> print reg.name_x
['CONSTANT', 'income', 'crime', 'lambda']

Hence, we find the same number of betas as of standard errors, which we calculate taking the square root of the diagonal of the variance-covariance matrix:

>>> print np.around(np.hstack((reg.betas,np.sqrt(reg.vm.diagonal()).reshape(4,1))),4)
[[ 47.9963  11.479 ]
 [  0.7105   0.3681]
 [ -0.5588   0.1616]
 [  0.4118   0.168 ]]

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

predyarray

nx1 array of predicted y values

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

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

pr2float

Pseudo R squared (squared correlation between y and ypred)

vmarray

Variance covariance matrix (kxk)

std_errarray

1xk array of standard errors of the betas

z_statlist of tuples

z statistic; each tuple contains the pair (statistic, p-value), where each is a float

xtxfloat

\(X'X\)

name_ystring

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

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

__init__(self, y, x, w, max_iter=1, epsilon=1e-05, step1c=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__(self, y, x, w[, max_iter, epsilon, …])

Initialize self.

Attributes

mean_y
std_y