pysal.model.spreg.TSLS

class pysal.model.spreg.TSLS(y, x, yend, q, w=None, 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]

Two stage least squares with results and diagnostics.

Parameters:
y : array

nx1 array for dependent variable

x : array

Two dimensional array with n rows and one column for each independent (exogenous) variable, excluding the constant

yend : array

Two dimensional array with n rows and one column for each endogenous variable

q : array

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)

w : pysal W object

Spatial weights object (required if running spatial diagnostics)

robust : string

If ‘white’, then a White consistent estimator of the variance-covariance matrix is given. If ‘hac’, then a HAC consistent estimator of the variance-covariance matrix is given. Default set to None.

gwk : pysal W object

Kernel spatial weights needed for HAC estimation. Note: matrix must have ones along the main diagonal.

sig2n_k : boolean

If True, then use n-k to estimate sigma^2. If False, use n.

spat_diag : boolean

If True, then compute Anselin-Kelejian test (requires w)

vm : boolean

If True, include variance-covariance matrix in summary results

name_y : string

Name of dependent variable for use in output

name_x : list of strings

Names of independent variables for use in output

name_yend : list of strings

Names of endogenous variables for use in output

name_q : list of strings

Names of instruments for use in output

name_w : string

Name of weights matrix for use in output

name_gwk : string

Name of kernel weights matrix for use in output

name_ds : string

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 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, but this can be overridden by passing constant=False.

>>> X = []
>>> X.append(db.by_col("INC"))
>>> X = np.array(X).T

In this case we consider HOVAL (home value) is an endogenous regressor. We tell the model that this is so by passing it in a different parameter from the exogenous variables (x).

>>> yd = []
>>> yd.append(db.by_col("HOVAL"))
>>> yd = np.array(yd).T

Because we have endogenous variables, to obtain a correct estimate of the model, we need to instrument for HOVAL. We use DISCBD (distance to the CBD) for this and hence put it in the instruments parameter, ‘q’.

>>> q = []
>>> q.append(db.by_col("DISCBD"))
>>> q = np.array(q).T

We are all set with the preliminars, we are good to run the model. In this case, we will need the variables (exogenous and endogenous) and the instruments. 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 = TSLS(y, X, yd, q, name_x=['inc'], name_y='crime', name_yend=['hoval'], name_q=['discbd'], name_ds='columbus')
>>> print reg.betas
[[ 88.46579584]
 [  0.5200379 ]
 [ -1.58216593]]
Attributes:
summary : string

Summary of regression results and diagnostics (note: use in conjunction with the print command)

betas : array

kx1 array of estimated coefficients

u : array

nx1 array of residuals

predy : array

nx1 array of predicted y values

n : integer

Number of observations

k : integer

Number of variables for which coefficients are estimated (including the constant)

kstar : integer

Number of endogenous variables.

y : array

nx1 array for dependent variable

x : array

Two dimensional array with n rows and one column for each independent (exogenous) variable, including the constant

yend : array

Two dimensional array with n rows and one column for each endogenous variable

q : array

Two dimensional array with n rows and one column for each external exogenous variable used as instruments

z : array

nxk array of variables (combination of x and yend)

h : array

nxl array of instruments (combination of x and q)

robust : string

Adjustment for robust standard errors

mean_y : float

Mean of dependent variable

std_y : float

Standard deviation of dependent variable

vm : array

Variance covariance matrix (kxk)

pr2 : float

Pseudo R squared (squared correlation between y and ypred)

utu : float

Sum of squared residuals

sig2 : float

Sigma squared used in computations

std_err : array

1xk array of standard errors of the betas

z_stat : list of tuples

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

ak_test : tuple

Anselin-Kelejian test; tuple contains the pair (statistic, p-value)

name_y : string

Name of dependent variable for use in output

name_x : list of strings

Names of independent variables for use in output

name_yend : list of strings

Names of endogenous variables for use in output

name_z : list of strings

Names of exogenous and endogenous variables for use in output

name_q : list of strings

Names of external instruments

name_h : list of strings

Names of all instruments used in ouput

name_w : string

Name of weights matrix for use in output

name_gwk : string

Name of kernel weights matrix for use in output

name_ds : string

Name of dataset for use in output

title : string

Name of the regression method used

sig2n : float

Sigma squared (computed with n in the denominator)

sig2n_k : float

Sigma squared (computed with n-k in the denominator)

hth : float

H’H

hthi : float

(H’H)^-1

varb : array

(Z’H (H’H)^-1 H’Z)^-1

zthhthi : array

Z’H(H’H)^-1

pfora1a2 : array

n(zthhthi)’varb

__init__(y, x, yend, q, w=None, 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, robust, gwk, …]) Initialize self.

Attributes

mean_y
pfora1a2
sig2n
sig2n_k
std_y
utu
vm