spreg.Probit¶

class spreg.Probit(y, x, w=None, slx_lags=0, slx_vars='All', optim='newton', bstart=False, scalem='phimean', predflag=False, maxiter=100, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, spat_diag=False, latex=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:

Pinkse Error [Pin04]
Kelejian and Prucha Moran’s I [KP01]
Pinkse & Slade Error [PS98]

Parameters:

xnumpy.ndarray or pandas object: nxk array of independent variables (assumed to be aligned with y)
ynumpy.ndarray or pandas.Series: nx1 array of dependent binary variable
wW: PySAL weights instance aligned with y
slx_lagsinteger: Number of spatial lags of X to include in the model specification. If slx_lags>0, the specification becomes of the SLX type.
slx_varsvariables to be lagged when slx_lags > 0: default = “All”, otherwise a list with Booleans indicating which variables must be lagged (True) or not (False)
optimstr: Optimization method. Default: ‘newton’ (Newton-Raphson). Alternatives: ‘ncg’ (Newton-CG), ‘bfgs’ (BFGS algorithm)
bstartlist: list with starting values for betas, default = False
scalemstr: Method to calculate the scale of the marginal effects. Default: ‘phimean’ (Mean of individual marginal effects) Alternative: ‘xmean’ (Marginal effects at variables mean)
predflagflag to print prediction table
maxiterint: Maximum number of iterations until optimizer stops
name_ystr: Name of dependent variable for use in output
name_xlist of strings: Names of independent variables for use in output
name_wstr: Name of weights matrix for use in output
name_dsstr: Name of dataset for use in output

Attributes:

xarray: Two dimensional array with n rows and one column for each independent (exogenous) variable, including the constant
xmeanarray: kx1 vector with means of explanatory variables (for use in slopes)
yarray: nx1 array of dependent variable
wspatial weights object
optimstr: optimization method
predflagflag to print prediction table (predtable)
maxiterint: maximum number of iterations
qarray: nx1 array of transformed dependent variable 2*y - 1
betasarray: kx1 array with estimated coefficients
bstartlist with starting values for betas or False
predyarray: nx1 array of predicted y values (probabilities)
nint: Number of observations
kint: Number of variables
vmarray: Variance-covariance matrix (kxk)
loglfloat: Log-Likelihhod of the estimation
xbpredicted value of linear index: nx1 array
predybinpredicted value as binary: =1 for predy > 0.5
phiynormal density at xb (phi function): nx1 array
u_naivenaive residuals y - predy: nx1 array
u_gengeneralized residuals: nx1 array
warningbool: if True Maximum number of iterations exceeded or gradient and/or function calls not changing.
std_errstandard errors of estimates
z_statlist of tuples: z statistic; each tuple contains the pair (statistic, p-value), where each is a float
predtabledictionary: includes margins and cells of actual and predicted values for discrete choice model
fita dictionary containing various measures of fit: TPR : true positive rate (sensitivity, recall, hit rate) TNR : true negative rate (specificity, selectivity) PREDPC : accuracy, percent correctly predicted BA : balanced accuracy
predpcfloat: Percent of y correctly predicted (legacy)
LRtestdictionary: contains the statistic for the null model (L0), the LR test(likr), the degrees of freedom (df) and the p-value (pvalue)
L0likelihood of null model
LRtuple (legacy): Likelihood Ratio test of all coefficients = 0 (test statistics, p-value)
mcfadrhoMcFadden rho statistics of fit
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)
slopes_std_errestimates of standard errors of marginal effects
slopes_z_stattuple with z-statistics and p-values for marginal effects
Pinkse_error: array with statistic and p-value: Lagrange Multiplier test against spatial error correlation. Implemented as presented in [Pin04]
KP_errorarray with statistic and p-value: Moran’s I type test against spatial error correlation. Implemented as presented in [KP01]
PS_errorarray with statistic and p-value: Lagrange Multiplier test against spatial error correlation. Implemented as presented in [PS98]
name_ystr: Name of dependent variable for use in output
name_xlist of strings: Names of independent variables for use in output
name_wstr: Name of weights matrix for use in output
name_dsstr: Name of dataset for use in output
titlestr: Name of the regression method used

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’

__init__(y, x, w=None, slx_lags=0, slx_vars='All', optim='newton', bstart=False, scalem='phimean', predflag=False, maxiter=100, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, spat_diag=False, latex=False)[source]¶

Methods

`__init__`(y, x[, w, slx_lags, slx_vars, ...])
`gradient`(par)
`hessian`(par)
`ll`(par)
`par_est`()

gradient(par)¶

hessian(par)¶

ll(par)¶

par_est()¶