spreg.OLS_Endog_Regimes¶

class spreg.OLS_Endog_Regimes(y, x, w, n_clusters=None, quorum=-1, trace=True, name_y=None, name_x=None, **kwargs)[source]¶

Ordinary least squares 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_dsstr: Name of dataset 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

predyarray

nx1 array of predicted y values

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)

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)

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)

r2float

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

ar2float

Adjusted R squared 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)

sig2MLfloat

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

f_stattuple

Statistic (float), p-value (float) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

logllfloat

Log likelihood 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 information criterion 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)

t_statlist of tuples

t 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)

mulCollifloat

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

jarque_beradictionary

‘jb’: Jarque-Bera statistic (float); ‘pvalue’: p-value (float); ‘df’: degrees of freedom (int) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

breusch_pagandictionary

‘bp’: Breusch-Pagan statistic (float); ‘pvalue’: p-value (float); ‘df’: degrees of freedom (int) Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

koenker_bassett: dictionary

‘kb’: Koenker-Bassett statistic (float); ‘pvalue’: p-value (float); ‘df’: degrees of freedom (int). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details).

whitedictionary

‘wh’: White statistic (float); ‘pvalue’: p-value (float); ‘df’: degrees of freedom (int). Only available in dictionary ‘multi’ when multiple regressions (see ‘multi’ below for details)

lm_errortuple

Lagrange multiplier test for spatial error model; 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)

lm_lagtuple

Lagrange multiplier test for spatial lag model; 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)

rlm_errortuple

Robust lagrange multiplier test for spatial error model; 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)

rlm_lagtuple

Robust lagrange multiplier test for spatial lag model; 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)

lm_sarmatuple

Lagrange multiplier test for spatial SARMA model; 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)

moran_restuple

Moran’s I for the residuals; tuple containing the triple (Moran’s I, standardized Moran’s I, p-value)

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 regime variable for use in the 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)

xtxfloat

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

xtxifloat

\((X'X)^{-1}\). 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_registr

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

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_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.

>>> olsr = OLS_Endog_Regimes(y=db['PRICE'], x=db[['NROOM','AGE','SQFT']], w=w, name_w="baltim_q.gal")

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

Alternatively, we can check individual attributes: >>> olsr.betas array([[26.24209866],

[ 2.40329959], [-0.24183707], [ 0.45714794], [19.84817747], [ 5.12117483], [-0.65466516], [ 1.10034154]])

>>> olsr.SSR
[68840.74965798721, 62741.55717492997]
>>> olsr.clusters
array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 0, 1, 0, 0, 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, 0, 1], dtype=int32)

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

>>> olsr = OLS_Endog_Regimes(y=db['PRICE'], x=db[['NROOM','AGE','SQFT']], w=w, n_clusters=2, name_w="baltim_q.gal")

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

Alternatively, we can check individual attributes as before: >>> olsr.betas array([[26.24209866],

[ 2.40329959], [-0.24183707], [ 0.45714794], [19.84817747], [ 5.12117483], [-0.65466516], [ 1.10034154]])

>>> olsr.SSR
[68840.74965798721]
>>> olsr.clusters
array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 1, 1, 0, 1, 0, 0, 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, 0, 1], dtype=int32)

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

Methods

__init__(y, x, w[, n_clusters, quorum, ...])

Attributes

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

property mean_y¶

property sig2n¶

property sig2n_k¶

property std_y¶

property utu¶

property vm¶