spreg.GM_Lag_Endog_Regimes

class spreg.GM_Lag_Endog_Regimes(y, x, w, n_clusters=None, quorum=-1, trace=True, name_y=None, name_x=None, **kwargs)

Spatial two stage least squares (S2SLS) with endogenous regimes. Based on the function skater_reg as shown in [AA24].

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

wpysal W object

Spatial weights object (required if running spatial diagnostics)

n_clustersint

Number of clusters to be used in the endogenous regimes. If None (default), the number of clusters will be chosen according to the function utils.optim_k using a method adapted from Mojena (1977)’s Rule Two

quorumint

Minimum number of observations in a cluster to be considered Must be at least larger than the number of variables in x Default value is 30 or 10*k, whichever is larger.

tracebool

Sets whether to store intermediate results of the clustering Hard-coded to True if n_clusters is None

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_gwkstr

Name of kernel 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

**kwargsadditional keyword arguments depending on the specific model

Attributes:

outputdataframe

regression results pandas dataframe

summarystr

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

betasarray

kx1 array of estimated coefficients

uarray

nx1 array of residuals

e_predarray

nx1 array of residuals (using reduced form)

predyarray

nx1 array of predicted y values

predy_earray

nx1 array of predicted y values (using reduced form)

ninteger

Number of observations

kinteger

Number of variables for which coefficients are estimated (including the constant) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

kstarinteger

Number of endogenous variables. 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)

yendarray

Two dimensional array with n rows and one column for each endogenous variable Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

qarray

Two dimensional array with n rows and one column for each external exogenous variable used as instruments Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

zarray

nxk array of variables (combination of x and yend) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

harray

nxl array of instruments (combination of x and q) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

robuststr

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

mean_yfloat

Mean of dependent variable

std_yfloat

Standard deviation of dependent variable

vmarray

Variance covariance matrix (kxk)

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)

utufloat

Sum of squared residuals

sig2float

Sigma squared used in computations 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)

ak_testtuple

Anselin-Kelejian test; tuple contains the pair (statistic, p-value) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

cfh_testtuple

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

name_ystr

Name of dependent variable for use in output

name_xlist of strings

Names of independent variables for use in output

name_yendlist of strings

Names of endogenous variables for use in output

name_zlist of strings

Names of exogenous and endogenous variables for use in output

name_qlist of strings

Names of external instruments

name_hlist of strings

Names of all instruments used in ouput

name_wstr

Name of weights matrix for use in output

name_gwkstr

Name of kernel 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)

sig2nfloat

Sigma squared (computed with n in the denominator)

sig2n_kfloat

Sigma squared (computed with n-k in the denominator)

hthfloat

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

hthifloat

\((H'H)^{-1}\). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

varbarray

\((Z'H (H'H)^{-1} H'Z)^{-1}\). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

zthhthiarray

\(Z'H(H'H)^{-1}\). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

pfora1a2array

n(zthhthi)’varb 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)

regimeslist

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

constant_regi: string

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

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

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

SSRlist

list with the total sum of squared residuals for the model considering all regimes for each of steps of number of regimes considered, starting with the solution with 2 regimes.

clustersint

Number of clusters considered in the endogenous regimes

_tracelist

List of dictionaries with the clustering results for each number of clusters tested. Only available if n_clusters is None or trace=True.

Examples

——–

>>> import libpysal

>>> import numpy as np

>>> np.set_printoptions(legacy=’1.25’) #to avoid printing issues with numpy floats

>>> import geopandas as gpd

>>> from spreg import OLS_Endog_Regimes

Open data on Baltimore house sales price and characteristics in Baltimore

from libpysal examples using geopandas.

>>> db = gpd.read_file(libpysal.examples.get_path(‘baltim.shp’))

We will create a weights matrix based on contiguity.

>>> w = libpysal.weights.Queen.from_dataframe(db, use_index=True)

>>> w.transform = “r”

For this example, we will use the ‘PRICE’ column as the dependent variable and

the ‘NROOM’, ‘AGE’, and ‘SQFT’ columns as independent variables.

At this point, we will let the model choose the number of clusters.

>>> reg = GM_Lag_Endog_Regimes(y=db[‘PRICE’], x=db[[‘NROOM’,’AGE’,’SQFT’]], w=w, name_w=”baltim_q.gal”)

The function `print(reg.summary)` can be used to visualize the results of the regression.

Alternatively, we can check individual attributes:

>>> reg.betas

array([[ 6.20932938],

[ 4.25581944], [-0.1468118 ], [ 0.40893082], [ 5.01866492], [ 4.84994184], [-0.55425337], [ 1.04577632], [ 0.05155043]])

>>> reg.SSR

[59784.06769835169, 56858.621800274515]

>>> reg.clusters

array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1,

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], dtype=int32)

We will now set the number of clusters to 2 and run the regression again.

>>> reg = GM_Lag_Endog_Regimes(y=db[‘PRICE’], x=db[[‘NROOM’,’AGE’,’SQFT’]], w=w, n_clusters=2, name_w=”baltim_q.gal”)

The function `print(reg.summary)` can be used to visualize the results of the regression.

Alternatively, we can check individual attributes as before:

>>> reg.betas

array([[ 6.20932938],

[ 4.25581944], [-0.1468118 ], [ 0.40893082], [ 5.01866492], [ 4.84994184], [-0.55425337], [ 1.04577632], [ 0.05155043]])

>>> reg.SSR

[59784.06769835169]

>>> reg.clusters

array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1,

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], dtype=int32)

__init__(y, x, w, n_clusters=None, quorum=-1, trace=True, name_y=None, name_x=None, **kwargs)

Methods

GM_Lag_Regimes_Multi(y, x, w_i, w, regi_ids)
__init__(y, x, w[, n_clusters, quorum, ...])
sp_att_reg(w_i, regi_ids, wy)

Attributes

mean_y
pfora1a2
sig2n
sig2n_k
std_y
utu
vm

GM_Lag_Regimes_Multi(y, x, w_i, w, regi_ids, cores=False, yend=None, q=None, w_lags=1, slx_lags=0, lag_q=True, robust=None, gwk=None, sig2n_k=False, cols2regi='all', spat_impacts=False, spat_diag=False, vm=False, name_y=None, name_x=None, name_yend=None, name_q=None, name_regimes=None, name_w=None, name_gwk=None, name_ds=None, latex=False, hard_bound=False)

property mean_y

property pfora1a2

property sig2n

property sig2n_k

sp_att_reg(w_i, regi_ids, wy)

property std_y

property utu

property vm