spreg.ML_Lag_Regimes¶

class spreg.ML_Lag_Regimes(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, slx_lags=0, slx_vars='all', regime_lag_sep=False, cores=False, spat_diag=True, spat_impacts='simple', vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None, latex=False)[source]¶

ML estimation of the spatial lag model with regimes (note no consistency checks, diagnostics or constants added) [Ans88].

Parameters:

ynumpy.ndarray or pandas.Series

nx1 array for dependent variable

xnumpy.ndarray or pandas object

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

regimeslist or pandas.Series

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

methodstr

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

slx_lagsinteger

Number of spatial lags of X to include in the model specification. If slx_lags>0, the specification becomes of the Spatial Durbin type.

slx_varseither “all” (default) or list of booleans to select x variables

to be lagged

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.

spat_diagbool

If True, then compute Common Factor Hypothesis test when applicable

spat_impactsstr or list

Include average direct impact (ADI), average indirect impact (AII),: and average total impact (ATI) in summary results. Options are ‘simple’, ‘full’, ‘power’, ‘all’ or None. See sputils.spmultiplier for more information.

coresbool

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

vmbool

if True, include variance-covariance matrix in summary results

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

name_regimesstr

Name of regimes variable for use in output

latexbool

Specifies if summary is to be printed in latex format

Attributes:

outputdataframe

regression results pandas dataframe

summarystr

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)

methodstr

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

cfh_testtuple

Common Factor Hypothesis test; tuple contains the pair (statistic, p-value). Only when it applies (see specific documentation).

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)

sp_multipliers: dict

Dictionary of spatial multipliers (if spat_impacts is not None) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

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

name_regimesstr

Name of regimes variable for use in output

titlestr

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

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
>>> from libpysal.examples import load_example
>>> from libpysal.weights import Queen
>>> from spreg import ML_Lag_Regimes
>>> import geopandas as gpd
>>> np.set_printoptions(suppress=True) #prevent scientific format
>>> baltimore = load_example('Baltimore')
>>> db = libpysal.io.open(baltimore.get_path("baltim.dbf"),'r')
>>> df = gpd.read_file(baltimore.get_path("baltim.shp"))
>>> 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
>>> w = Queen.from_dataframe(df)
>>> 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([[-14.5158],
       [  4.4923],
       [ -0.0336],
       [  0.3541],
       [ -3.601 ],
       [  3.8736],
       [ -0.1747],
       [  0.8238],
       [  0.525 ]])
>>> "{0:.6f}".format(mllag.rho)
'0.524971'
>>> "{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([ 48.6818,   2.4524,   0.0052,   0.0663,  71.4439,   3.2837,
         0.0118,   0.0498,   0.0042, 409.1225])
>>> np.around(np.diag(mllag.vm), decimals=4)
array([48.6818,  2.4524,  0.0052,  0.0663, 71.4439,  3.2837,  0.0118,
        0.0498,  0.0042])
>>> "{0:.6f}".format(mllag.sig2)
'204.827093'
>>> "{0:.6f}".format(mllag.logll)
'-867.086467'
>>> "{0:.6f}".format(mllag.aic)
'1752.172934'
>>> "{0:.6f}".format(mllag.schwarz)
'1782.339657'
>>> mllag.title
'MAXIMUM LIKELIHOOD SPATIAL LAG - REGIMES (METHOD = full)'

__init__(y, x, regimes, w=None, constant_regi='many', cols2regi='all', method='full', epsilon=1e-07, slx_lags=0, slx_vars='all', regime_lag_sep=False, cores=False, spat_diag=True, spat_impacts='simple', vm=False, name_y=None, name_x=None, name_w=None, name_ds=None, name_regimes=None, latex=False)[source]¶

Methods

`ML_Lag_Regimes_Multi`(y, x, w_i, w, regi_ids, ...)
`__init__`(y, x, regimes[, w, constant_regi, ...])

Attributes

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

ML_Lag_Regimes_Multi(y, x, w_i, w, regi_ids, slx_lags, cores, cols2regi, method, epsilon, spat_diag, spat_impacts, vm, name_y, name_x, name_regimes, name_w, name_ds, latex)[source]¶

property mean_y¶

property sig2n¶

property sig2n_k¶

property std_y¶

property utu¶

property vm¶