spreg.Probit¶

class spreg.Probit(y, x, w=None, optim='newton', scalem='phimean', maxiter=100, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, spat_diag=False)[source]

Classic non-spatial Probit and spatial diagnostics. The class includes a printout that formats all the results and tests in a nice format.

The diagnostics for spatial dependence currently implemented are:

Parameters
xarray

nxk array of independent variables (assumed to be aligned with y)

yarray

nx1 array of dependent binary variable

wW

PySAL weights instance aligned with y

optimstring

Optimization method. Default: ‘newton’ (Newton-Raphson). Alternatives: ‘ncg’ (Newton-CG), ‘bfgs’ (BFGS algorithm)

scalemstring

Method to calculate the scale of the marginal effects. Default: ‘phimean’ (Mean of individual marginal effects) Alternative: ‘xmean’ (Marginal effects at variables mean)

maxiterint

Maximum number of iterations until optimizer stops

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 libpysal to perform all the analysis.

>>> import numpy as np
>>> import libpysal
>>> np.set_printoptions(suppress=True) #prevent scientific format


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.

>>> dbf = libpysal.io.open(libpysal.examples.get_path('columbus.dbf'),'r')


Extract the CRIME column (crime) from the DBF file and make it the dependent variable for the regression. Note that libpysal requires this to be an numpy array of shape (n, 1) as opposed to the also common shape of (n, ) that other packages accept. Since we want to run a probit model and for this example we use the Columbus data, we also need to transform the continuous CRIME variable into a binary variable. As in [McM92], we define y = 1 if CRIME > 40.

>>> y = np.array([dbf.by_col('CRIME')]).T
>>> y = (y>40).astype(float)


Extract HOVAL (home values) and INC (income) vectors from the DBF to be used as independent variables in the regression. Note that libpysal 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.

>>> names_to_extract = ['INC', 'HOVAL']
>>> x = np.array([dbf.by_col(name) for name in names_to_extract]).T


Since we want to the test the probit model for spatial dependence, 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 use columbus.gal, which contains contiguity relationships between the observations in the Columbus dataset we are using throughout this example. Note that, in order to read the file, not only to open it, we need to append ‘.read()’ at the end of the command.

>>> w = libpysal.io.open(libpysal.examples.get_path("columbus.gal"), 'r').read()


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. In libpysal, 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.

>>> from spreg import Probit
>>> model = Probit(y, x, w=w, name_y='crime', name_x=['income','home value'], name_ds='columbus', name_w='columbus.gal')


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.

>>> np.around(model.betas, decimals=6)
array([[ 3.353811],
[-0.199653],
[-0.029514]])

>>> np.around(model.vm, decimals=6)
array([[ 0.852814, -0.043627, -0.008052],
[-0.043627,  0.004114, -0.000193],
[-0.008052, -0.000193,  0.00031 ]])


Since we have provided a spatial weigths matrix, the diagnostics for spatial dependence have also been computed. We can access them and their p-values individually:

>>> tests = np.array([['Pinkse_error','KP_error','PS_error']])
>>> stats = np.array([[model.Pinkse_error[0],model.KP_error[0],model.PS_error[0]]])
>>> pvalue = np.array([[model.Pinkse_error[1],model.KP_error[1],model.PS_error[1]]])
>>> print(np.hstack((tests.T,np.around(np.hstack((stats.T,pvalue.T)),6))))
[['Pinkse_error' '3.131719' '0.076783']
['KP_error' '1.721312' '0.085194']
['PS_error' '2.558166' '0.109726']]


Or we can easily obtain a full summary of all the results nicely formatted and ready to be printed simply by typing ‘print model.summary’

Attributes
xarray

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

yarray

nx1 array of dependent variable

betasarray

kx1 array with estimated coefficients

predyarray

nx1 array of predicted y values

nint

Number of observations

kint

Number of variables

vmarray

Variance-covariance matrix (kxk)

z_statlist of tuples

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

xmeanarray

Mean of the independent variables (kx1)

predpcfloat

Percent of y correctly predicted

loglfloat

Log-Likelihhod of the estimation

scalemstring

Method to calculate the scale of the marginal effects.

scalefloat

Scale of the marginal effects.

slopesarray

Marginal effects of the independent variables (k-1x1)

slopes_vmarray

Variance-covariance matrix of the slopes (k-1xk-1)

LRtuple

Likelihood Ratio test of all coefficients = 0 (test statistics, p-value)

Pinkse_error: float

Lagrange Multiplier test against spatial error correlation. Implemented as presented in [Pin04]

KP_errorfloat

Moran’s I type test against spatial error correlation. Implemented as presented in [KP01]

PS_errorfloat

Lagrange Multiplier test against spatial error correlation. Implemented as presented in [PS98]

warningboolean

if True Maximum number of iterations exceeded or gradient and/or function calls not changing.

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__(y, x, w=None, optim='newton', scalem='phimean', maxiter=100, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, spat_diag=False)[source]

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

Methods

 __init__(y, x[, w, optim, scalem, maxiter, …]) Initialize self. gradient(par) hessian(par) ll(par)

Attributes

property KP_error
property LR
property PS_error
property Pinkse_error
gradient(par)
hessian(par)
ll(par)
par_est()
property phiy
property predpc
property predy
property scale
property slopes
property slopes_std_err
property slopes_vm
property slopes_z_stat
property u_gen
property u_naive
property vm
property xb
property xmean
property z_stat