spreg.ML_Lag_Regimes¶

class spreg.ML_Lag_Regimes(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_lag_sep=False, regime_err_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 lag model with regimes (note no consistency checks, diagnostics or constants added) [Ans88].

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

regimeslist

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

constant_regi: string

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)

cols2regilist, ‘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.

wSparse matrix

Spatial weights sparse matrix

methodstring

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

epsilonfloat

tolerance criterion in mimimize_scalar function and inverse_product

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.

coresboolean

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

spat_diagboolean

if True, include spatial diagnostics (not implemented yet)

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_wstring

Name of weights matrix for use in output

name_dsstring

Name of dataset for use in output

name_regimesstring

Name of regimes variable for use in output

Examples

Open data baltim.dbf using pysal and create the variables matrices and weights matrix.

>>> import numpy as np
>>> import libpysal
>>> from libpysal import examples
>>> db =  libpysal.io.open(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:

>>> mllag = ML_Lag_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(mllag.betas, decimals=4)
array([[-15.0059],
       [  4.496 ],
       [ -0.0318],
       [  0.35  ],
       [ -4.5404],
       [  3.9219],
       [ -0.1702],
       [  0.8194],
       [  0.5385]])
>>> "{0:.6f}".format(mllag.rho)
'0.538503'
>>> "{0:.6f}".format(mllag.mean_y)
'44.307180'
>>> "{0:.6f}".format(mllag.std_y)
'23.606077'
>>> np.around(np.diag(mllag.vm1), decimals=4)
array([  47.42  ,    2.3953,    0.0051,    0.0648,   69.6765,    3.2066,
          0.0116,    0.0486,    0.004 ,  390.7274])
>>> np.around(np.diag(mllag.vm), decimals=4)
array([ 47.42  ,   2.3953,   0.0051,   0.0648,  69.6765,   3.2066,
         0.0116,   0.0486,   0.004 ])
>>> "{0:.6f}".format(mllag.sig2)
'200.044334'
>>> "{0:.6f}".format(mllag.logll)
'-864.985056'
>>> "{0:.6f}".format(mllag.aic)
'1747.970112'
>>> "{0:.6f}".format(mllag.schwarz)
'1778.136835'
>>> mllag.title
'MAXIMUM LIKELIHOOD SPATIAL LAG - REGIMES (METHOD = full)'

Attributes

summarystring

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

betasarray

(k+1)x1 array of estimated coefficients (rho first)

rhofloat

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

uarray

nx1 array of residuals

predyarray

nx1 array of predicted y values

ninteger

Number of observations

kinteger

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)

yarray

nx1 array for dependent variable

xarray

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)

methodstring

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

epsilonfloat

tolerance criterion used in minimize_scalar function and inverse_product

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

vmarray

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

vm1array

Variance covariance matrix (k+2 x k+2), includes sig2 Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

sig2float

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

logllfloat

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

aicfloat

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

schwarzfloat

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

predy_earray

predicted values from reduced form

e_predarray

prediction errors using reduced form predicted values

pr2float

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

pr2_efloat

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

std_errarray

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

z_statlist 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_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

name_regimesstring

Name of regimes variable for use in output

titlestring

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

regimeslist

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

cols2regilist, ‘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.

regime_err_sep: boolean

always set to False - kept for compatibility with other regime models

krint

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)

kfint

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

nrint

Number of different regimes in the ‘regimes’ list

multidictionary

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

Methods

ML_Lag_Regimes_Multi

__init__(self, y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, regime_lag_sep=False, regime_err_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

`ML_Lag_Regimes_Multi`(self, y, x, w_i, w, …)
`__init__`(self, y, x, regimes[, w, …])	Initialize self.

Attributes

`mean_y`
`sig2n`
`sig2n_k`
`std_y`
`utu`
`vm`