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Spatial Panel Models with Fixed Effects¶
This notebook uses the Panel_FE_Lag and Panel_FE_Error classes.
[1]:
import numpy
import libpysal
import spreg
Open data on NCOVR US County Homicides (3085 areas).
First, extract the HR (homicide rates) data in the 70’s, 80’s and 90’s as the dependent variable.
Data can also be passed in the long format instead of wide format.
i.e. a vector with \(n \times t\) rows and a single column for the dependent variable, and
a matrix of dimension \(n \times (t \ast k)\) for the independent variables
Then, extract RD and PS as independent variables in the regression.
[2]:
# Open data on NCOVR US County Homicides (3085 areas).
nat = libpysal.examples.load_example("NCOVR")
db = libpysal.io.open(nat.get_path("NAT.dbf"), "r")
# Create spatial weight matrix
nat_shp = libpysal.examples.get_path("NAT.shp")
w = libpysal.weights.Queen.from_shapefile(nat_shp)
w.transform = 'r'
# Define dependent variable
name_y = ["HR70", "HR80", "HR90"]
y = numpy.array([db.by_col(name) for name in name_y]).T
# Define independent variables
name_x = ["RD70", "RD80", "RD90", "PS70", "PS80", "PS90"]
x = numpy.array([db.by_col(name) for name in name_x]).T
Spatial Lag model¶
Let’s estimate a spatial lag panel model with fixed effects:
\[y = \rho Wy + X\beta + \mu_i + e\]
[ ]:
fe_lag = spreg.Panel_FE_Lag(y, x, w, name_y=name_y, name_x=name_x, name_ds="NAT")
[4]:
print(fe_lag.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: MAXIMUM LIKELIHOOD SPATIAL LAG PANEL - FIXED EFFECTS
-----------------------------------------------------------------------
Data set : NAT
Weights matrix : unknown
Dependent Variable : HR Number of Observations: 9255
Mean dependent var : 0.0000 Number of Variables : 3
S.D. dependent var : 3.9228 Degrees of Freedom : 9252
Pseudo R-squared : 0.0319
Spatial Pseudo R-squared: 0.0079
Sigma-square ML : 14.935 Log likelihood : -67936.533
S.E of regression : 3.865 Akaike info criterion : 135879.066
Schwarz criterion : 135900.465
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
RD 0.8005886 0.1614474 4.9588189 0.0000007
PS -2.6003523 0.4935486 -5.2686851 0.0000001
W_HR 0.1903043 0.0159991 11.8947008 0.0000000
------------------------------------------------------------------------------------
Warning: Assuming panel is in wide format.
y[:, 0] refers to T0, y[:, 1] refers to T1, etc.
x[:, 0:T] refers to T periods of k1, x[:, T+1:2T] refers to k2, etc.
================================ END OF REPORT =====================================
[5]:
numpy.around(fe_lag.betas, decimals=4)
[5]:
array([[ 0.8006],
[-2.6004],
[ 0.1903]])
Data can also be in ‘long’ format:¶
[6]:
y_long = y.reshape((y.shape[0]*y.shape[1],1), order='F')
x_long = x.reshape((x.shape[0]*3,2), order='F')
fe_lag_long = spreg.Panel_FE_Lag(y_long, x_long, w, name_y=name_y, name_x=name_x, name_ds="NAT")
print(fe_lag_long.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: MAXIMUM LIKELIHOOD SPATIAL LAG PANEL - FIXED EFFECTS
-----------------------------------------------------------------------
Data set : NAT
Weights matrix : unknown
Dependent Variable : HR Number of Observations: 9255
Mean dependent var : 0.0000 Number of Variables : 3
S.D. dependent var : 3.9228 Degrees of Freedom : 9252
Pseudo R-squared : 0.0319
Spatial Pseudo R-squared: 0.0079
Sigma-square ML : 14.935 Log likelihood : -67936.533
S.E of regression : 3.865 Akaike info criterion : 135879.066
Schwarz criterion : 135900.465
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
RD 0.8005886 0.1614474 4.9588189 0.0000007
PS -2.6003523 0.4935486 -5.2686851 0.0000001
W_HR 0.1903043 0.0159991 11.8947008 0.0000000
------------------------------------------------------------------------------------
Warning: Assuming panel is in long format.
y[0:N] refers to T0, y[N+1:2N] refers to T1, etc.
x[0:N] refers to T0, x[N+1:2N] refers to T1, etc.
================================ END OF REPORT =====================================
Spatial Error model¶
Now, let’s estimate a spatial error panel model with fixed effects:
\[y = X\beta + \mu_i + v\]
where
\[v = \lambda W v + e\]
[7]:
fe_error = spreg.Panel_FE_Error(
y, x, w, name_y=name_y, name_x=name_x, name_ds="NAT"
)
[8]:
print(fe_error.summary)
REGRESSION
----------
SUMMARY OF OUTPUT: MAXIMUM LIKELIHOOD SPATIAL ERROR PANEL - FIXED EFFECTS
-------------------------------------------------------------------------
Data set : NAT
Weights matrix : unknown
Dependent Variable : HR Number of Observations: 9255
Mean dependent var : 0.0000 Number of Variables : 2
S.D. dependent var : 3.9228 Degrees of Freedom : 9253
Pseudo R-squared : 0.0084
Sigma-square ML : 14.923 Log likelihood : -67934.005
S.E of regression : 3.863 Akaike info criterion : 135872.010
Schwarz criterion : 135886.276
------------------------------------------------------------------------------------
Variable Coefficient Std.Error z-Statistic Probability
------------------------------------------------------------------------------------
RD 0.8697923 0.1718029 5.0627323 0.0000004
PS -2.9660674 0.5444783 -5.4475397 0.0000001
lambda 0.1943460 0.0160253 12.1274197 0.0000000
------------------------------------------------------------------------------------
Warning: Assuming panel is in wide format.
y[:, 0] refers to T0, y[:, 1] refers to T1, etc.
x[:, 0:T] refers to T periods of k1, x[:, T+1:2T] refers to k2, etc.
================================ END OF REPORT =====================================
[9]:
numpy.around(fe_error.betas, decimals=4)
[9]:
array([[ 0.8698],
[-2.9661],
[ 0.1943]])