# spreg.GM_Combo_Hom¶

class spreg.GM_Combo_Hom(y, x, yend=None, q=None, w=None, w_lags=1, lag_q=True, max_iter=1, epsilon=1e-05, A1='hom_sc', 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 homoskedasticity and endogenous variables, with results and diagnostics; based on Drukker et al. (2013) [DEP13], following Anselin (2011) [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 necessary)

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.

A1string

If A1=’het’, then the matrix A1 is defined as in [ADKP10]. If A1=’hom’, then as in [Ans11]. If A1=’hom_sc’ (default), then as in [DEP13] and [DPR13].

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_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 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) 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 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'


Example only with spatial lag

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_Hom(y, X, w=w, A1='hom_sc', name_x=['inc'],            name_y='hoval', name_yend=['crime'], name_q=['discbd'],            name_ds='columbus')
>>> print np.around(np.hstack((reg.betas,np.sqrt(reg.vm.diagonal()).reshape(4,1))),4)
[[ 10.1254  15.2871]
[  1.5683   0.4407]
[  0.1513   0.4048]
[  0.2103   0.4226]]


This class also allows the user to run a spatial lag+error model with the extra feature of including non-spatial endogenous regressors. This means that, in addition to the spatial lag and error, we consider some of the variables on the right-hand 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_Hom(y, X, yd, q, w=w, A1='hom_sc',             name_ds='columbus')
>>> betas = np.array([['CONSTANT'],['inc'],['crime'],['W_hoval'],['lambda']])
>>> print np.hstack((betas, np.around(np.hstack((reg.betas, np.sqrt(reg.vm.diagonal()).reshape(5,1))),5)))
[['CONSTANT' '111.7705' '67.75191']
['inc' '-0.30974' '1.16656']
['crime' '-1.36043' '0.6841']
['W_hoval' '-0.52908' '0.84428']
['lambda' '0.60116' '0.18605']]

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))

sig2float

Sigma squared used in computations (based on filtered residuals)

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

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=1e-05, A1='hom_sc', 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