pysal.model.spreg.ML_Error_Regimes

class pysal.model.spreg.ML_Error_Regimes(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_err_sep=False, regime_lag_sep=False, cores=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None)[source]

ML estimation of the spatial error model with regimes (note no consistency checks, diagnostics or constants added); Anselin (1988) [Anselin1988]

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

regimes : list

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.

constant_regi: [‘one’, ‘many’]

Switcher controlling the constant term setup. It may take the following values:

  • ‘one’: a vector of ones is appended to x and held
    constant across regimes
  • ‘many’: a vector of ones is appended to x and considered
    different per regime (default)
cols2regi : list, ‘all’

Argument indicating whether each column of x should be considered as different per regime or held constant across regimes (False). If a list, k booleans indicating for each variable the option (True if one per regime, False to be held constant). If ‘all’ (default), all the variables vary by regime.

w : Sparse matrix

Spatial weights sparse matrix

method : string

if ‘full’, brute force calculation (full matrix expressions) if ‘ord’, Ord eigenvalue computation if ‘LU’, LU sparse matrix decomposition

epsilon : float

tolerance criterion in mimimize_scalar function and inverse_product

regime_err_sep : boolean

If True, a separate regression is run for each regime.

regime_lag_sep : boolean

Always False, kept for consistency in function call, ignored.

cores : boolean

Specifies if multiprocessing is to be used Default: no multiprocessing, cores = False Note: Multiprocessing may not work on all platforms.

spat_diag : boolean

if True, include spatial diagnostics (not implemented yet)

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_w : string

Name of weights matrix for use in output

name_ds : string

Name of dataset for use in output

name_regimes : string

Name of regimes variable for use in output

Attributes:
summary : string

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

betas : array

(k+1)x1 array of estimated coefficients (lambda last)

lam : float

estimate of spatial autoregressive coefficient Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

u : array

nx1 array of residuals

e_filtered : array

nx1 array of spatially filtered 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, excluding the rho) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

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 Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

method : string

log Jacobian method if ‘full’: brute force (full matrix computations) if ‘ord’, Ord eigenvalue computation if ‘LU’, LU sparse matrix decomposition

epsilon : float

tolerance criterion used in minimize_scalar function and inverse_product

mean_y : float

Mean of dependent variable

std_y : float

Standard deviation of dependent variable

vm : array

Variance covariance matrix (k+1 x k+1), all coefficients

vm1 : array

variance covariance matrix for lambda, sigma (2 x 2) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

sig2 : float

Sigma squared used in computations Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

logll : float

maximized log-likelihood (including constant terms) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

pr2 : float

Pseudo R squared (squared correlation between y and ypred) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

std_err : array

1xk array of standard errors of the betas Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

z_stat : list of tuples

z statistic; each tuple contains the pair (statistic, p-value), where each is a float Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

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_w : string

Name of weights matrix for use in output

name_ds : string

Name of dataset for use in output

name_regimes : string

Name of regimes variable for use in output

title : string

Name of the regression method used Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

regimes : list

List of n values with the mapping of each observation to a regime. Assumed to be aligned with ‘x’.

constant_regi: [‘one’, ‘many’]

Ignored if regimes=False. Constant option for regimes. Switcher controlling the constant term setup. It may take the following values:

  • ‘one’: a vector of ones is appended to x and held
    constant across regimes
  • ‘many’: a vector of ones is appended to x and considered
    different per regime
cols2regi : list, ‘all’

Ignored if regimes=False. Argument indicating whether each column of x should be considered as different per regime or held constant across regimes (False). If a list, k booleans indicating for each variable the option (True if one per regime, False to be held constant). If ‘all’, all the variables vary by regime.

regime_lag_sep : boolean

If True, the spatial parameter for spatial lag is also computed according to different regimes. If False (default), the spatial parameter is fixed accross regimes.

kr : int

Number of variables/columns to be “regimized” or subject to change by regime. These will result in one parameter estimate by regime for each variable (i.e. nr parameters per variable)

kf : int

Number of variables/columns to be considered fixed or global across regimes and hence only obtain one parameter estimate

nr : int

Number of different regimes in the ‘regimes’ list

multi : dictionary

Only available when multiple regressions are estimated, i.e. when regime_err_sep=True and no variable is fixed across regimes. Contains all attributes of each individual regression

Examples
________
Open data baltim.dbf using pysal and create the variables matrices and weights matrix.
>>> import numpy as np
>>> import pysal.lib
>>> db = pysal.lib.io.open(pysal.lib.examples.get_path(“baltim.dbf”),’r’)
>>> ds_name = “baltim.dbf”
>>> y_name = “PRICE”
>>> y = np.array(db.by_col(y_name)).T
>>> y.shape = (len(y),1)
>>> x_names = [“NROOM”,”AGE”,”SQFT”]
>>> x = np.array([db.by_col(var) for var in x_names]).T
>>> ww = ps.open(ps.examples.get_path(“baltim_q.gal”))
>>> w = ww.read()
>>> ww.close()
>>> w_name = “baltim_q.gal”
>>> w.transform = ‘r’
Since in this example we are interested in checking whether the results vary
by regimes, we use CITCOU to define whether the location is in the city or
outside the city (in the county):
>>> regimes = db.by_col(“CITCOU”)
Now we can run the regression with all parameters:
>>> mlerr = ML_Error_Regimes(y,x,regimes,w=w,name_y=y_name,name_x=x_names, name_w=w_name,name_ds=ds_name,name_regimes=”CITCOU”)
>>> np.around(mlerr.betas, decimals=4)
array([[ -2.3949],

[ 4.8738], [ -0.0291], [ 0.3328], [ 31.7962], [ 2.981 ], [ -0.2371], [ 0.8058], [ 0.6177]])

>>> “{0:.6f}”.format(mlerr.lam)
‘0.617707’
>>> “{0:.6f}”.format(mlerr.mean_y)
‘44.307180’
>>> “{0:.6f}”.format(mlerr.std_y)
‘23.606077’
>>> np.around(mlerr.vm1, decimals=4)
array([[ 0.005 , -0.3535],

[ -0.3535, 441.3039]])

>>> np.around(np.diag(mlerr.vm), decimals=4)
array([ 58.5055, 2.4295, 0.0072, 0.0639, 80.5925, 3.161 ,

0.012 , 0.0499, 0.005 ])

>>> np.around(mlerr.sig2, decimals=4)
array([[ 209.6064]])
>>> “{0:.6f}”.format(mlerr.logll)
‘-870.333106’
>>> “{0:.6f}”.format(mlerr.aic)
‘1756.666212’
>>> “{0:.6f}”.format(mlerr.schwarz)
‘1783.481077’
>>> mlerr.title
‘MAXIMUM LIKELIHOOD SPATIAL ERROR - REGIMES (METHOD = full)’

Methods

get_x_lag  
__init__(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_err_sep=False, regime_lag_sep=False, cores=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None)[source]

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

Methods

__init__(y, x, regimes[, w, constant_regi, …]) Initialize self.
get_x_lag(w, regimes_att)

Attributes

mean_y
sig2n
sig2n_k
std_y
utu
vm