Notebook Outline:

Set up Cells

In [1]:
import sys
sys.path.append("C:/Users/msachde1/Downloads/Research/Development/mgwr")
In [2]:
import warnings
warnings.filterwarnings("ignore")
import pandas as pd
import numpy as np

from mgwr.gwr import GWR
from spglm.family import Gaussian, Binomial, Poisson
from mgwr.gwr import MGWR
from mgwr.sel_bw import Sel_BW
import multiprocessing as mp
pool = mp.Pool()
from scipy import linalg
import numpy.linalg as la
from scipy import sparse as sp
from scipy.sparse import linalg as spla
from spreg.utils import spdot, spmultiply
from scipy import special
import libpysal as ps
import seaborn as sns
import matplotlib.pyplot as plt
from copy import deepcopy
import copy
from collections import namedtuple
import spglm

Clearwater Landslides Dataset

Clearwater data - downloaded from link: https://sgsup.asu.edu/sparc/multiscale-gwr

In [3]:
data_p = pd.read_csv("C:/Users/msachde1/Downloads/logistic_mgwr_data/landslides.csv")
In [4]:
data_p.head()
Out[4]:
UserID X Y Elev Slope SinAspct CosAspct AbsSouth Landslid DistStrm
0 1 616168.5625 5201076.5 1450.475 27.44172 0.409126 -0.912478 24.1499 1 8.506
1 2 624923.8125 5201008.5 1567.476 21.88343 -0.919245 -0.393685 66.8160 1 15.561
2 3 615672.0000 5199187.5 1515.065 38.81030 -0.535024 -0.844837 32.3455 1 41.238
3 4 615209.3125 5199112.0 1459.827 26.71631 -0.828548 -0.559918 55.9499 1 17.539
4 5 616354.6875 5198945.5 1379.442 27.55271 -0.872281 -0.489005 60.7248 1 35.023

Univariate example

GWR Binomial model with independent variable, x = slope

In [5]:
coords = list(zip(data_p['X'],data_p['Y']))
y = np.array(data_p['Landslid']).reshape((-1,1)) 
elev = np.array(data_p['Elev']).reshape((-1,1))
slope = np.array(data_p['Slope']).reshape((-1,1))
SinAspct = np.array(data_p['SinAspct']).reshape(-1,1)
CosAspct = np.array(data_p['CosAspct']).reshape(-1,1)
X = np.hstack([elev,slope,SinAspct,CosAspct])
x = CosAspct

X_std = (X-X.mean(axis=0))/X.std(axis=0)
x_std = (x-x.mean(axis=0))/x.std(axis=0)
y_std = (y-y.mean(axis=0))/y.std(axis=0)
In [6]:
bw=Sel_BW(coords,y,x_std,family=Binomial(),constant=False).search()
gwr_mod=GWR(coords,y,x_std,bw=bw,family=Binomial(),constant=False).fit()
bw
Out[6]:
108.0
Running the function with family = Binomial()

Bandwidths check

In [7]:
selector = Sel_BW(coords,y,x_std,family=Binomial(),multi=True,constant=False)
selector.search(verbose=True)

Current iteration: 1 ,SOC: 0.0752521
Bandwidths: 108.0
Current iteration: 2 ,SOC: 0.0213201
Bandwidths: 184.0
Current iteration: 3 ,SOC: 5.8e-05
Bandwidths: 184.0
Current iteration: 4 ,SOC: 1e-06
Bandwidths: 184.0
Out[7]:
array([184.])
In [8]:
mgwr_mod = MGWR(coords, y,x_std,selector,family=Binomial(),constant=False).fit()





















Parameter check












In [9]:



    


mgwr_mod.bic



    















    
Out[9]:








325.23949237389036



















In [10]:



    


gwr_mod.bic



    















    
Out[10]:








338.19722049287054





















Multivariate example












In [12]:



    


bw=Sel_BW(coords,y,X_std,family=Binomial(),constant=True).search()
gwr_mod=GWR(coords,y,X_std,bw=bw,family=Binomial(),constant=True).fit()
bw



    















    
Out[12]:








121.0





















Bandwidth check












In [13]:



    


selector = Sel_BW(coords,y,X_std,family=Binomial(),multi=True,constant=True)
selector.search(verbose=True)



    















    






Current iteration: 1 ,SOC: 0.116124
Bandwidths: 43.0, 62.0, 191.0, 100.0, 108.0
Current iteration: 2 ,SOC: 0.0266811
Bandwidths: 43.0, 106.0, 210.0, 100.0, 184.0
Current iteration: 3 ,SOC: 0.0008147
Bandwidths: 43.0, 106.0, 210.0, 100.0, 184.0
Current iteration: 4 ,SOC: 5.28e-05
Bandwidths: 43.0, 106.0, 210.0, 100.0, 184.0
Current iteration: 5 ,SOC: 5.3e-06
Bandwidths: 43.0, 106.0, 210.0, 100.0, 184.0










    
Out[13]:








array([ 43., 106., 210., 100., 184.])



















In [14]:



    


mgwr_mod = MGWR(coords, y,X_std,selector,family=Binomial(),constant=True).fit()



    















    






 
 















    


























AIC, AICc, BIC check












In [15]:



    


gwr_mod.aicc, mgwr_mod.aicc



    















    
Out[15]:








(264.9819711678866, 251.85376815296377)





















Global model check












In [16]:



    


selector=Sel_BW(coords,y,X_std,multi=True,family=Binomial(),constant=True)
selector.search(verbose=True,multi_bw_min=[239,239,239,239,239], multi_bw_max=[239,239,239,239,239])



    















    






Current iteration: 1 ,SOC: 0.6120513
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0
Current iteration: 2 ,SOC: 0.0594775
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0
Current iteration: 3 ,SOC: 0.0025897
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0
Current iteration: 4 ,SOC: 0.0001289
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0
Current iteration: 5 ,SOC: 1.17e-05
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0
Current iteration: 6 ,SOC: 1.2e-06
Bandwidths: 239.0, 239.0, 239.0, 239.0, 239.0










    
Out[16]:








array([239., 239., 239., 239., 239.])



















In [17]:



    


mgwr_mod = MGWR(coords, y,X_std,selector,family=Binomial(),constant=True).fit()



    















    






 
 















    
























In [18]:



    


gwr_mod.summary()



    















    






===========================================================================
Model type                                                         Binomial
Number of observations:                                                 239
Number of covariates:                                                     5

Global Regression Results
---------------------------------------------------------------------------
Deviance:                                                           266.246
Log-likelihood:                                                    -133.123
AIC:                                                                276.246
AICc:                                                               276.504
BIC:                                                              -1015.246
Percent deviance explained:                                           0.182
Adj. percent deviance explained:                                      0.168

Variable                              Est.         SE  t(Est/SE)    p-value
------------------------------- ---------- ---------- ---------- ----------
X0                                   0.389      0.150      2.591      0.010
X1                                  -0.784      0.166     -4.715      0.000
X2                                   0.654      0.168      3.881      0.000
X3                                   0.039      0.149      0.264      0.792
X4                                  -0.371      0.156     -2.381      0.017

Geographically Weighted Regression (GWR) Results
---------------------------------------------------------------------------
Spatial kernel:                                           Adaptive bisquare
Bandwidth used:                                                     121.000

Diagnostic information
---------------------------------------------------------------------------
Effective number of parameters (trace(S)):                           23.263
Degree of freedom (n - trace(S)):                                   215.737
Log-likelihood:                                                    -106.599
AIC:                                                                259.725
AICc:                                                               264.982
BIC:                                                                340.598
Percent deviance explained:                                         0.345
Adjusted percent deviance explained:                                0.274
Adj. alpha (95%):                                                     0.011
Adj. critical t value (95%):                                          2.571

Summary Statistics For GWR Parameter Estimates
---------------------------------------------------------------------------
Variable                   Mean        STD        Min     Median        Max
-------------------- ---------- ---------- ---------- ---------- ----------
X0                        0.459      0.360     -0.360      0.436      1.232
X1                       -0.824      0.479     -2.128     -0.729     -0.095
X2                        0.567      0.390     -0.030      0.600      1.328
X3                        0.103      0.270     -0.473      0.183      0.565
X4                       -0.331      0.247     -1.118     -0.287      0.096
===========================================================================




















In [19]:



    


np.mean(mgwr_mod.params,axis=0)



    















    
Out[19]:








array([ 0.19936242, -0.3251776 ,  0.32069312,  0.04295657, -0.20408904])



















In [20]:



    


mgwr_mod.bic, gwr_mod.bic



    















    
Out[20]:








(303.9521120546862, 340.5982180538755)