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Skater Regression

This notebook shows the use of the Skater Regression funcion (Skater_reg), introduced by Anselin & Amaral (2021). For more information on the method, check:

https://www.researchgate.net/publication/353411566_Endogenous_Spatial_Regimes

In this example, in addition to the required packages, we will use geopandas to load the data and matplotlib to plot the results. Alternatively, PySAL’s own IO could also be used to load the data.

[1]:
# Required imports
import libpysal as ps
import numpy as np
import spreg
from spreg.skater_reg import Skater_reg

# Optional imports
import matplotlib.pyplot as plt
import geopandas as gpd

We use Messner et al. (2000) data on homicides and selected socio-economic characteristics for continental U.S. counties to exemplify the use of Skater_reg. It can be downloaded from PySAL’s examples repository.

[2]:
# Load the example from PySAL
ps.examples.load_example("NCOVR")
data = gpd.read_file(ps.examples.get_path('NAT.shp')).set_index('FIPS')

# Set depedent and independent variables and the W matrix.
y = data['HR90'].to_numpy()
x = data[['RD90','PS90','UE90']].to_numpy()
w = ps.weights.Queen.from_dataframe(data, use_index=True)

Skater_reg by default uses Euclidean distance to compute the Minimum Spanning Tree (MST). Therefore, we standardize the variables that will be used to compute the MST before calling the main Skater_reg function. Here, we use the X variables to compute the MST. Alternative specifications can be used.

We set the number of clusters to 20 and minimum quorum to 100.

[3]:
%%time
# Standardize the variables to be used to compute the minimum spanning tree (could add/remove any variable)
x_std = (x - np.mean(x,axis=0)) / np.std(x,axis=0)

# Call the Skater_reg method based on OLS
results = Skater_reg().fit(20, w, x_std, {'reg':spreg.OLS,'y':y,'x':x}, quorum=100)
CPU times: user 1min 16s, sys: 31.6 s, total: 1min 48s
Wall time: 25.3 s

The intermediate steps are stored in the attibute _trace. We can use this information to plot the decrease in the total sum of squared residuals by number of clusters. This information can be helpful to select the number of desired clusters.

[4]:
trace = [results._trace[i][1][2] for i in range(1,len(results._trace))]
fig, ax = plt.subplots()
ax.plot(list(range(2,len(trace)+2)), trace, '-o', color='black', linewidth=2)

ax.set(xlabel='Number of clusters', ylabel='Total sum of squared residuals')
ax.grid()

plt.show()
../_images/notebooks_skater_reg_9_0.png

Let’s say we choose 12 clusters. We can plot the results using geopandas and matplotlib.

[5]:
data["cl_regions"] = results._trace[11][0]
data.plot(column="cl_regions", categorical=True, legend=True, cmap='Paired').axis("off")
[5]:
(-127.6195011138916, -64.0817699432373, 23.735178565979005, 50.59252300262451)
../_images/notebooks_skater_reg_11_1.png

With the cluster allocations and selected number of clusters, we can call the Regimes methods in Spreg to get the full regression results and Chow tests on the stability of the coefficients accross the 12 different clusters.

[6]:
reg = spreg.OLS_Regimes(y,x,
      regimes=results._trace[11][0], w=w, name_y=['HR90'], name_x=['RD90','PS90','UE90'], name_regimes='skater_reg')
print(reg.summary)
REGRESSION
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 0
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  0_['HR90']                Number of Observations:         604
Mean dependent var  :      2.4577                Number of Variables   :           4
S.D. dependent var  :      3.9266                Degrees of Freedom    :         600
R-squared           :      0.3305
Adjusted R-squared  :      0.3271
Sum squared residual:    6224.952                F-statistic           :     98.7116
Sigma-square        :      10.375                Prob(F-statistic)     :   6.109e-52
S.E. of regression  :       3.221                Log likelihood        :   -1561.528
Sigma-square ML     :      10.306                Akaike info criterion :    3131.057
S.E of regression ML:      3.2103                Schwarz criterion     :    3148.671

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          0_CONSTANT       4.0851876       0.4756999       8.5877407       0.0000000
              0_RD90       3.1288181       0.2856649      10.9527571       0.0000000
              0_PS90       1.4553321       0.1760078       8.2685645       0.0000000
              0_UE90       0.0530250       0.0612926       0.8651115       0.3873233
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            7.255

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2       20184.603           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          69.424           0.0000
Koenker-Bassett test              3           4.695           0.1956
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 1
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  1_['HR90']                Number of Observations:         180
Mean dependent var  :      2.6269                Number of Variables   :           4
S.D. dependent var  :      4.5592                Degrees of Freedom    :         176
R-squared           :      0.1473
Adjusted R-squared  :      0.1328
Sum squared residual:    3172.661                F-statistic           :     10.1339
Sigma-square        :      18.026                Prob(F-statistic)     :   3.424e-06
S.E. of regression  :       4.246                Log likelihood        :    -513.652
Sigma-square ML     :      17.626                Akaike info criterion :    1035.304
S.E of regression ML:      4.1983                Schwarz criterion     :    1048.076

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          1_CONSTANT       1.6802968       1.0041720       1.6733157       0.0960416
              1_RD90       0.9214816       0.7386502       1.2475210       0.2138639
              1_PS90       0.5520464       0.3817853       1.4459601       0.1499668
              1_UE90       0.3793060       0.1012117       3.7476508       0.0002418
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            6.525

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2        4249.029           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3           6.927           0.0743
Koenker-Bassett test              3           0.565           0.9044
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 2
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  2_['HR90']                Number of Observations:         105
Mean dependent var  :      5.4586                Number of Variables   :           4
S.D. dependent var  :      3.9328                Degrees of Freedom    :         101
R-squared           :      0.6004
Adjusted R-squared  :      0.5885
Sum squared residual:     642.756                F-statistic           :     50.5868
Sigma-square        :       6.364                Prob(F-statistic)     :   4.794e-20
S.E. of regression  :       2.523                Log likelihood        :    -244.108
Sigma-square ML     :       6.121                Akaike info criterion :     496.217
S.E of regression ML:      2.4742                Schwarz criterion     :     506.832

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          2_CONSTANT       2.9279569       1.6500241       1.7744934       0.0789946
              2_RD90       3.8978472       0.8119511       4.8005936       0.0000055
              2_PS90       2.5952604       0.2458875      10.5546660       0.0000000
              2_UE90       0.3236171       0.1945793       1.6631633       0.0993799
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           15.160

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2           6.807           0.0333

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          15.329           0.0016
Koenker-Bassett test              3          14.809           0.0020
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 3
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  3_['HR90']                Number of Observations:         157
Mean dependent var  :      3.2521                Number of Variables   :           4
S.D. dependent var  :      3.4925                Degrees of Freedom    :         153
R-squared           :      0.3735
Adjusted R-squared  :      0.3612
Sum squared residual:    1192.118                F-statistic           :     30.4049
Sigma-square        :       7.792                Prob(F-statistic)     :   1.785e-15
S.E. of regression  :       2.791                Log likelihood        :    -381.912
Sigma-square ML     :       7.593                Akaike info criterion :     771.824
S.E of regression ML:      2.7556                Schwarz criterion     :     784.049

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          3_CONSTANT       1.6648327       1.6499048       1.0090477       0.3145449
              3_RD90       2.5911850       0.5446873       4.7571975       0.0000045
              3_PS90       1.7951113       0.2645028       6.7867381       0.0000000
              3_UE90       0.2831519       0.1896309       1.4931734       0.1374511
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           17.037

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2         700.804           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3         128.095           0.0000
Koenker-Bassett test              3          23.069           0.0000
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 4
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  4_['HR90']                Number of Observations:         157
Mean dependent var  :      5.2565                Number of Variables   :           4
S.D. dependent var  :      7.5670                Degrees of Freedom    :         153
R-squared           :      0.0718
Adjusted R-squared  :      0.0536
Sum squared residual:    8291.273                F-statistic           :      3.9445
Sigma-square        :      54.191                Prob(F-statistic)     :    0.009592
S.E. of regression  :       7.361                Log likelihood        :    -534.160
Sigma-square ML     :      52.811                Akaike info criterion :    1076.321
S.E of regression ML:      7.2671                Schwarz criterion     :    1088.546

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          4_CONSTANT       6.5333323       2.4673414       2.6479239       0.0089474
              4_RD90       2.7602351       1.0586310       2.6073627       0.0100275
              4_PS90      -0.6252142       0.6065058      -1.0308463       0.3042397
              4_UE90      -0.0983422       0.2825469      -0.3480561       0.7282764
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            9.215

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2       10522.321           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3         397.444           0.0000
Koenker-Bassett test              3          19.450           0.0002
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 5
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  5_['HR90']                Number of Observations:         416
Mean dependent var  :      3.5350                Number of Variables   :           4
S.D. dependent var  :      3.5289                Degrees of Freedom    :         412
R-squared           :      0.2384
Adjusted R-squared  :      0.2328
Sum squared residual:    3936.025                F-statistic           :     42.9870
Sigma-square        :       9.553                Prob(F-statistic)     :   3.458e-24
S.E. of regression  :       3.091                Log likelihood        :   -1057.705
Sigma-square ML     :       9.462                Akaike info criterion :    2123.409
S.E of regression ML:      3.0760                Schwarz criterion     :    2139.532

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          5_CONSTANT       3.6580644       0.7883611       4.6400874       0.0000047
              5_RD90       2.1705064       0.3732128       5.8157339       0.0000000
              5_PS90       1.6485127       0.2143249       7.6916535       0.0000000
              5_UE90      -0.0049898       0.0843801      -0.0591343       0.9528738
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           11.124

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2        2163.820           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3         295.778           0.0000
Koenker-Bassett test              3          48.598           0.0000
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 6
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  6_['HR90']                Number of Observations:         105
Mean dependent var  :      6.9902                Number of Variables   :           4
S.D. dependent var  :      7.7137                Degrees of Freedom    :         101
R-squared           :      0.5133
Adjusted R-squared  :      0.4989
Sum squared residual:    3011.570                F-statistic           :     35.5107
Sigma-square        :      29.818                Prob(F-statistic)     :   9.373e-16
S.E. of regression  :       5.461                Log likelihood        :    -325.192
Sigma-square ML     :      28.682                Akaike info criterion :     658.384
S.E of regression ML:      5.3555                Schwarz criterion     :     669.000

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          6_CONSTANT      12.6762323       2.3973782       5.2875396       0.0000007
              6_RD90       7.2357749       0.8959392       8.0761894       0.0000000
              6_PS90       3.0087836       0.5687185       5.2904618       0.0000007
              6_UE90      -0.9087647       0.4285148      -2.1207310       0.0363931
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           10.336

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2        1082.543           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          69.868           0.0000
Koenker-Bassett test              3           8.330           0.0397
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 7
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  7_['HR90']                Number of Observations:         212
Mean dependent var  :      6.7045                Number of Variables   :           4
S.D. dependent var  :      7.5062                Degrees of Freedom    :         208
R-squared           :      0.6513
Adjusted R-squared  :      0.6463
Sum squared residual:    4145.470                F-statistic           :    129.5007
Sigma-square        :      19.930                Prob(F-statistic)     :   2.429e-47
S.E. of regression  :       4.464                Log likelihood        :    -615.973
Sigma-square ML     :      19.554                Akaike info criterion :    1239.945
S.E of regression ML:      4.4220                Schwarz criterion     :    1253.372

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          7_CONSTANT       6.8749278       1.4815715       4.6402943       0.0000062
              7_RD90       5.0735729       0.4720012      10.7490683       0.0000000
              7_PS90       4.3257745       0.4290443      10.0823502       0.0000000
              7_UE90      -0.1901823       0.2136345      -0.8902227       0.3743748
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           10.840

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2          23.086           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          68.023           0.0000
Koenker-Bassett test              3          50.360           0.0000
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 8
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  8_['HR90']                Number of Observations:         142
Mean dependent var  :      6.9674                Number of Variables   :           4
S.D. dependent var  :      7.7639                Degrees of Freedom    :         138
R-squared           :      0.0816
Adjusted R-squared  :      0.0616
Sum squared residual:    7805.895                F-statistic           :      4.0858
Sigma-square        :      56.564                Prob(F-statistic)     :    0.008156
S.E. of regression  :       7.521                Log likelihood        :    -485.973
Sigma-square ML     :      54.971                Akaike info criterion :     979.945
S.E of regression ML:      7.4142                Schwarz criterion     :     991.769

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          8_CONSTANT       8.9134518       2.2205952       4.0139922       0.0000975
              8_RD90       3.1669956       1.0249618       3.0898670       0.0024224
              8_PS90       0.9219418       0.7333370       1.2571872       0.2108094
              8_UE90      -0.2902235       0.3083686      -0.9411576       0.3482687
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            7.818

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2         211.413           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          16.332           0.0010
Koenker-Bassett test              3           4.771           0.1893
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 9
---------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  :  9_['HR90']                Number of Observations:         494
Mean dependent var  :      9.4357                Number of Variables   :           4
S.D. dependent var  :      6.1868                Degrees of Freedom    :         490
R-squared           :      0.3161
Adjusted R-squared  :      0.3120
Sum squared residual:   12904.325                F-statistic           :     75.5098
Sigma-square        :      26.335                Prob(F-statistic)     :   3.675e-40
S.E. of regression  :       5.132                Log likelihood        :   -1506.863
Sigma-square ML     :      26.122                Akaike info criterion :    3021.726
S.E of regression ML:      5.1110                Schwarz criterion     :    3038.536

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
          9_CONSTANT      10.2257744       0.7060239      14.4836089       0.0000000
              9_RD90       4.9173048       0.3601681      13.6528046       0.0000000
              9_PS90       2.7435413       0.3773269       7.2709932       0.0000000
              9_UE90      -0.5158999       0.1027098      -5.0228862       0.0000007
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            7.112

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2         164.804           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          93.891           0.0000
Koenker-Bassett test              3          45.305           0.0000
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 10
----------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  : 10_['HR90']                Number of Observations:         322
Mean dependent var  :     10.9368                Number of Variables   :           4
S.D. dependent var  :      7.1069                Degrees of Freedom    :         318
R-squared           :      0.1980
Adjusted R-squared  :      0.1904
Sum squared residual:   13003.178                F-statistic           :     26.1676
Sigma-square        :      40.890                Prob(F-statistic)     :   3.738e-15
S.E. of regression  :       6.395                Log likelihood        :   -1052.340
Sigma-square ML     :      40.383                Akaike info criterion :    2112.680
S.E of regression ML:      6.3547                Schwarz criterion     :    2127.779

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
         10_CONSTANT       8.9613419       1.1548606       7.7596741       0.0000000
             10_RD90       3.1036861       0.4676112       6.6373221       0.0000000
             10_PS90       2.0054035       0.4775095       4.1997143       0.0000347
             10_UE90      -0.1659300       0.1618652      -1.0251118       0.3060896
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER            8.728

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2         805.242           0.0000

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3         271.848           0.0000
Koenker-Bassett test              3          60.502           0.0000
----------

SUMMARY OF OUTPUT: ORDINARY LEAST SQUARES ESTIMATION - REGIME 11
----------------------------------------------------------------
Data set            :     unknown
Weights matrix      :     unknown
Dependent Variable  : 11_['HR90']                Number of Observations:         191
Mean dependent var  :     12.6163                Number of Variables   :           4
S.D. dependent var  :      6.4910                Degrees of Freedom    :         187
R-squared           :      0.2010
Adjusted R-squared  :      0.1882
Sum squared residual:    6396.303                F-statistic           :     15.6792
Sigma-square        :      34.205                Prob(F-statistic)     :   3.882e-09
S.E. of regression  :       5.848                Log likelihood        :    -606.337
Sigma-square ML     :      33.488                Akaike info criterion :    1220.674
S.E of regression ML:      5.7869                Schwarz criterion     :    1233.683

------------------------------------------------------------------------------------
            Variable     Coefficient       Std.Error     t-Statistic     Probability
------------------------------------------------------------------------------------
         11_CONSTANT      10.6523809       1.8667675       5.7063244       0.0000000
             11_RD90       2.8884391       0.5972275       4.8364133       0.0000028
             11_PS90       0.2205890       0.5966193       0.3697316       0.7120008
             11_UE90      -0.0296635       0.3154386      -0.0940388       0.9251790
------------------------------------------------------------------------------------
Regimes variable: skater_reg

REGRESSION DIAGNOSTICS
MULTICOLLINEARITY CONDITION NUMBER           10.444

TEST ON NORMALITY OF ERRORS
TEST                             DF        VALUE           PROB
Jarque-Bera                       2          16.443           0.0003

DIAGNOSTICS FOR HETEROSKEDASTICITY
RANDOM COEFFICIENTS
TEST                             DF        VALUE           PROB
Breusch-Pagan test                3          18.499           0.0003
Koenker-Bassett test              3          11.542           0.0091

REGIMES DIAGNOSTICS - CHOW TEST
                 VARIABLE        DF        VALUE           PROB
                 CONSTANT        11         110.297           0.0000
                     PS90        11          95.473           0.0000
                     RD90        11          75.733           0.0000
                     UE90        11          52.373           0.0000
              Global test        44         532.110           0.0000
================================ END OF REPORT =====================================
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