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pacman::p_load(sf, tidyverse, funModeling, blorr, corrplot, ggpubr, spdep, GWmodel, tmap, skimr, caret)Logistic Regression for Osun State, Nigeria Water Point
Understanding the implementation of Spatial Logistic Regression on real-life dataset.
geospatial
sf
spdep
tmap
clustering
Overview
The Data
Getting Started
Before we get started, it is important for us to install the necessary R packages into R and launch these R packages into R environment.
The code chunks below installs and launches these R packages into R environment.
Geospatial Data Wrangling
Importing RDS data
In this exercise, we will focus on the Water Point at Osun state. The RDS file is provided as part of the In-Class Exercise.
Exploratory Data Analysis (EDA)
In the section, you will learn how to use statistical graphics functions of funModeling package to perform EDA.
EDA using statistical graphics
From the EDA, we will be able to understand the distribution of our independent variable.
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Osun_wp_sf %>%
freq(input = "status")
status frequency percentage cumulative_perc
1 TRUE 2642 55.5 55.5
2 FALSE 2118 44.5 100.0Using tmap, we are able to plot the distribution of Functional and Non-Functional water point within the state.
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tm_shape(Osun) +
tm_polygons(alpha = 0.4) +
tm_shape(Osun_wp_sf) +
tm_dots(col = "status",
alpha = 0.6) +
tm_view(set.zoom.limits = c(9,12))
The skim() function from the skimr package allow us to explore the columns with a summary of missing variables.
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Osun_wp_sf %>%
skim()| Name | Piped data |
| Number of rows | 4760 |
| Number of columns | 75 |
| _______________________ | |
| Column type frequency: | |
| character | 47 |
| logical | 5 |
| numeric | 23 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| source | 0 | 1.00 | 5 | 44 | 0 | 2 | 0 |
| report_date | 0 | 1.00 | 22 | 22 | 0 | 42 | 0 |
| status_id | 0 | 1.00 | 2 | 7 | 0 | 3 | 0 |
| water_source_clean | 0 | 1.00 | 8 | 22 | 0 | 3 | 0 |
| water_source_category | 0 | 1.00 | 4 | 6 | 0 | 2 | 0 |
| water_tech_clean | 24 | 0.99 | 9 | 23 | 0 | 3 | 0 |
| water_tech_category | 24 | 0.99 | 9 | 15 | 0 | 2 | 0 |
| facility_type | 0 | 1.00 | 8 | 8 | 0 | 1 | 0 |
| clean_country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| clean_adm1 | 0 | 1.00 | 3 | 5 | 0 | 5 | 0 |
| clean_adm2 | 0 | 1.00 | 3 | 14 | 0 | 35 | 0 |
| clean_adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| clean_adm4 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| installer | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management_clean | 1573 | 0.67 | 5 | 37 | 0 | 7 | 0 |
| status_clean | 0 | 1.00 | 9 | 32 | 0 | 7 | 0 |
| pay | 0 | 1.00 | 2 | 39 | 0 | 7 | 0 |
| fecal_coliform_presence | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| subjective_quality | 0 | 1.00 | 18 | 20 | 0 | 4 | 0 |
| activity_id | 4757 | 0.00 | 36 | 36 | 0 | 3 | 0 |
| scheme_id | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| wpdx_id | 0 | 1.00 | 12 | 12 | 0 | 4760 | 0 |
| notes | 0 | 1.00 | 2 | 96 | 0 | 3502 | 0 |
| orig_lnk | 4757 | 0.00 | 84 | 84 | 0 | 1 | 0 |
| photo_lnk | 41 | 0.99 | 84 | 84 | 0 | 4719 | 0 |
| country_id | 0 | 1.00 | 2 | 2 | 0 | 1 | 0 |
| data_lnk | 0 | 1.00 | 79 | 96 | 0 | 2 | 0 |
| water_point_history | 0 | 1.00 | 142 | 834 | 0 | 4750 | 0 |
| clean_country_id | 0 | 1.00 | 3 | 3 | 0 | 1 | 0 |
| country_name | 0 | 1.00 | 7 | 7 | 0 | 1 | 0 |
| water_source | 0 | 1.00 | 8 | 30 | 0 | 4 | 0 |
| water_tech | 0 | 1.00 | 5 | 37 | 0 | 20 | 0 |
| adm2 | 0 | 1.00 | 3 | 14 | 0 | 33 | 0 |
| adm3 | 4760 | 0.00 | NA | NA | 0 | 0 | 0 |
| management | 1573 | 0.67 | 5 | 47 | 0 | 7 | 0 |
| adm1 | 0 | 1.00 | 4 | 5 | 0 | 4 | 0 |
| New Georeferenced Column | 0 | 1.00 | 16 | 35 | 0 | 4760 | 0 |
| lat_lon_deg | 0 | 1.00 | 13 | 32 | 0 | 4760 | 0 |
| public_data_source | 0 | 1.00 | 84 | 102 | 0 | 2 | 0 |
| converted | 0 | 1.00 | 53 | 53 | 0 | 1 | 0 |
| created_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| updated_timestamp | 0 | 1.00 | 22 | 22 | 0 | 2 | 0 |
| Geometry | 0 | 1.00 | 33 | 37 | 0 | 4760 | 0 |
| ADM2_EN | 0 | 1.00 | 3 | 14 | 0 | 30 | 0 |
| ADM2_PCODE | 0 | 1.00 | 8 | 8 | 0 | 30 | 0 |
| ADM1_EN | 0 | 1.00 | 4 | 4 | 0 | 1 | 0 |
| ADM1_PCODE | 0 | 1.00 | 5 | 5 | 0 | 1 | 0 |
Variable type: logical
| skim_variable | n_missing | complete_rate | mean | count |
|---|---|---|---|---|
| rehab_year | 4760 | 0 | NaN | : |
| rehabilitator | 4760 | 0 | NaN | : |
| is_urban | 0 | 1 | 0.39 | FAL: 2884, TRU: 1876 |
| latest_record | 0 | 1 | 1.00 | TRU: 4760 |
| status | 0 | 1 | 0.56 | TRU: 2642, FAL: 2118 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| row_id | 0 | 1.00 | 68550.48 | 10216.94 | 49601.00 | 66874.75 | 68244.50 | 69562.25 | 471319.00 | ▇▁▁▁▁ |
| lat_deg | 0 | 1.00 | 7.68 | 0.22 | 7.06 | 7.51 | 7.71 | 7.88 | 8.06 | ▁▂▇▇▇ |
| lon_deg | 0 | 1.00 | 4.54 | 0.21 | 4.08 | 4.36 | 4.56 | 4.71 | 5.06 | ▃▆▇▇▂ |
| install_year | 1144 | 0.76 | 2008.63 | 6.04 | 1917.00 | 2006.00 | 2010.00 | 2013.00 | 2015.00 | ▁▁▁▁▇ |
| fecal_coliform_value | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| distance_to_primary_road | 0 | 1.00 | 5021.53 | 5648.34 | 0.01 | 719.36 | 2972.78 | 7314.73 | 26909.86 | ▇▂▁▁▁ |
| distance_to_secondary_road | 0 | 1.00 | 3750.47 | 3938.63 | 0.15 | 460.90 | 2554.25 | 5791.94 | 19559.48 | ▇▃▁▁▁ |
| distance_to_tertiary_road | 0 | 1.00 | 1259.28 | 1680.04 | 0.02 | 121.25 | 521.77 | 1834.42 | 10966.27 | ▇▂▁▁▁ |
| distance_to_city | 0 | 1.00 | 16663.99 | 10960.82 | 53.05 | 7930.75 | 15030.41 | 24255.75 | 47934.34 | ▇▇▆▃▁ |
| distance_to_town | 0 | 1.00 | 16726.59 | 12452.65 | 30.00 | 6876.92 | 12204.53 | 27739.46 | 44020.64 | ▇▅▃▃▂ |
| rehab_priority | 2654 | 0.44 | 489.33 | 1658.81 | 0.00 | 7.00 | 91.50 | 376.25 | 29697.00 | ▇▁▁▁▁ |
| water_point_population | 4 | 1.00 | 513.58 | 1458.92 | 0.00 | 14.00 | 119.00 | 433.25 | 29697.00 | ▇▁▁▁▁ |
| local_population_1km | 4 | 1.00 | 2727.16 | 4189.46 | 0.00 | 176.00 | 1032.00 | 3717.00 | 36118.00 | ▇▁▁▁▁ |
| crucialness_score | 798 | 0.83 | 0.26 | 0.28 | 0.00 | 0.07 | 0.15 | 0.35 | 1.00 | ▇▃▁▁▁ |
| pressure_score | 798 | 0.83 | 1.46 | 4.16 | 0.00 | 0.12 | 0.41 | 1.24 | 93.69 | ▇▁▁▁▁ |
| usage_capacity | 0 | 1.00 | 560.74 | 338.46 | 300.00 | 300.00 | 300.00 | 1000.00 | 1000.00 | ▇▁▁▁▅ |
| days_since_report | 0 | 1.00 | 2692.69 | 41.92 | 1483.00 | 2688.00 | 2693.00 | 2700.00 | 4645.00 | ▁▇▁▁▁ |
| staleness_score | 0 | 1.00 | 42.80 | 0.58 | 23.13 | 42.70 | 42.79 | 42.86 | 62.66 | ▁▁▇▁▁ |
| location_id | 0 | 1.00 | 235865.49 | 6657.60 | 23741.00 | 230638.75 | 236199.50 | 240061.25 | 267454.00 | ▁▁▁▁▇ |
| cluster_size | 0 | 1.00 | 1.05 | 0.25 | 1.00 | 1.00 | 1.00 | 1.00 | 4.00 | ▇▁▁▁▁ |
| lat_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| lon_deg_original | 4760 | 0.00 | NaN | NA | NA | NA | NA | NA | NA | |
| count | 0 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | ▁▁▇▁▁ |
Next, we will filter the dependent variable to remove any NA rows. We will also change the class of the usage_capacity from numeric to factor.
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Osun_wp_sf_clean <- Osun_wp_sf %>%
filter_at (vars(status,
distance_to_city,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean),
all_vars(!is.na(.))) %>%
mutate(usage_capacity = as.factor(usage_capacity))Correlation Matrix
Before performing the correlation matrix, we will filter the required columns and dropping the geometry column.
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Osun_wp<- Osun_wp_sf_clean %>%
select(c(7,35:39,42:43, 46:47, 57)) %>%
st_drop_geometry()We will use the corrplot.mixed() from the corrplot package to examine the correlation between the variables.
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cluster_vars.cor = cor(
Osun_wp[,2:7])
corrplot.mixed(cluster_vars.cor,
lower = "ellipse",
upper = "number",
tl.pos = "lt",
diag = "l",
tl.col = "black"
)
Logistic Regression
We will use the glm() function to perform logistic regression on our variables.
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model <- glm (status ~ distance_to_primary_road +
distance_to_city +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sf_clean,
family = binomial(link = "logit"))Visualising Logistic Regression Output
Instead of using the base R report, we will use the blr_regress() function from the blorr package.
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blr_regress(model) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4744 TRUE
------------------------------------------------------------------------
Response Summary
--------------------------------------------------------
Outcome Frequency Outcome Frequency
--------------------------------------------------------
0 2114 1 2642
--------------------------------------------------------
Maximum Likelihood Estimates
-----------------------------------------------------------------------------------------------
Parameter DF Estimate Std. Error z value Pr(>|z|)
-----------------------------------------------------------------------------------------------
(Intercept) 1 0.3887 0.1124 3.4588 5e-04
distance_to_primary_road 1 0.0000 0.0000 -0.7153 0.4744
distance_to_city 1 0.0000 0.0000 -4.7574 0.0000
distance_to_secondary_road 1 0.0000 0.0000 -0.5530 0.5802
distance_to_tertiary_road 1 1e-04 0.0000 4.6708 0.0000
distance_to_town 1 0.0000 0.0000 -4.9170 0.0000
water_point_population 1 -5e-04 0.0000 -11.3686 0.0000
local_population_1km 1 3e-04 0.0000 19.2953 0.0000
usage_capacity1000 1 -0.6230 0.0697 -8.9366 0.0000
is_urbanTRUE 1 -0.2971 0.0819 -3.6294 3e-04
water_source_cleanProtected Shallow Well 1 0.5040 0.0857 5.8783 0.0000
water_source_cleanProtected Spring 1 1.2882 0.4388 2.9359 0.0033
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7347 Somers' D 0.4693
% Discordant 0.2653 Gamma 0.4693
% Tied 0.0000 Tau-a 0.2318
Pairs 5585188 c 0.7347
---------------------------------------------------------------From the output, we can identify that distance_to_primary_road and distance_to_secondary_road obtained p-value > 0.05 and therefore can be considered not statistically significant. We will then remove these variable for future analysis.
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blr_regress(model_clean) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4746 TRUE
------------------------------------------------------------------------
Response Summary
--------------------------------------------------------
Outcome Frequency Outcome Frequency
--------------------------------------------------------
0 2114 1 2642
--------------------------------------------------------
Maximum Likelihood Estimates
-----------------------------------------------------------------------------------------------
Parameter DF Estimate Std. Error z value Pr(>|z|)
-----------------------------------------------------------------------------------------------
(Intercept) 1 0.3540 0.1055 3.3541 8e-04
distance_to_city 1 0.0000 0.0000 -5.2022 0.0000
distance_to_tertiary_road 1 1e-04 0.0000 4.9096 0.0000
distance_to_town 1 0.0000 0.0000 -5.4660 0.0000
water_point_population 1 -5e-04 0.0000 -11.3902 0.0000
local_population_1km 1 3e-04 0.0000 19.4069 0.0000
usage_capacity1000 1 -0.6206 0.0697 -8.9081 0.0000
is_urbanTRUE 1 -0.2667 0.0747 -3.5690 4e-04
water_source_cleanProtected Shallow Well 1 0.4947 0.0850 5.8228 0.0000
water_source_cleanProtected Spring 1 1.2790 0.4384 2.9174 0.0035
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7349 Somers' D 0.4697
% Discordant 0.2651 Gamma 0.4697
% Tied 0.0000 Tau-a 0.2320
Pairs 5585188 c 0.7349
---------------------------------------------------------------Show the code
blr_confusion_matrix(model_clean, cutoff = 0.5)Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
0 1300 743
1 814 1899
Accuracy : 0.6726
No Information Rate : 0.4445
Kappa : 0.3348
McNemars's Test P-Value : 0.0761
Sensitivity : 0.7188
Specificity : 0.6149
Pos Pred Value : 0.7000
Neg Pred Value : 0.6363
Prevalence : 0.5555
Detection Rate : 0.3993
Detection Prevalence : 0.5704
Balanced Accuracy : 0.6669
Precision : 0.7000
Recall : 0.7188
'Positive' Class : 1Converting to Spatial Class
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Osun_wp_sp <- Osun_wp_sf_clean %>%
select (c(status,
distance_to_city,
distance_to_tertiary_road,
distance_to_town,
water_point_population,
local_population_1km,
usage_capacity,
is_urban,
water_source_clean)) %>%
as_Spatial()
Osun_wp_spclass : SpatialPointsDataFrame
features : 4756
extent : 182502.4, 290751, 340054.1, 450905.3 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=4 +lon_0=8.5 +k=0.99975 +x_0=670553.98 +y_0=0 +a=6378249.145 +rf=293.465 +towgs84=-92,-93,122,0,0,0,0 +units=m +no_defs
variables : 9
names : status, distance_to_city, distance_to_tertiary_road, distance_to_town, water_point_population, local_population_1km, usage_capacity, is_urban, water_source_clean
min values : 0, 53.0461399623541, 0.017815121653488, 30.0019777713073, 0, 0, 1000, 0, Borehole
max values : 1, 47934.343603562, 10966.2705628969, 44020.6393368124, 29697, 36118, 300, 1, Protected Spring Calculating the optimal fixed bandwidth
Using the function bw.ggwr(), we will derive the optimal fixed bandwidth to be used for the spatial logistic regression.
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bw.fixed <- bw.ggwr (status ~ distance_to_city +
distance_to_tertiary_road +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sp,
family = "binomial",
approach = "AIC",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE)Take a cup of tea and have a break, it will take a few minutes.
-----A kind suggestion from GWmodel development group
Iteration Log-Likelihood:(With bandwidth: 95768.67 )
=========================
0 -2890
1 -2837
2 -2830
3 -2829
4 -2829
5 -2829
Fixed bandwidth: 95768.67 AICc value: 5681.18
Iteration Log-Likelihood:(With bandwidth: 59200.13 )
=========================
0 -2878
1 -2820
2 -2812
3 -2810
4 -2810
5 -2810
Fixed bandwidth: 59200.13 AICc value: 5645.901
Iteration Log-Likelihood:(With bandwidth: 36599.53 )
=========================
0 -2854
1 -2790
2 -2777
3 -2774
4 -2774
5 -2774
6 -2774
Fixed bandwidth: 36599.53 AICc value: 5585.354
Iteration Log-Likelihood:(With bandwidth: 22631.59 )
=========================
0 -2810
1 -2732
2 -2711
3 -2707
4 -2707
5 -2707
6 -2707
Fixed bandwidth: 22631.59 AICc value: 5481.877
Iteration Log-Likelihood:(With bandwidth: 13998.93 )
=========================
0 -2732
1 -2635
2 -2604
3 -2597
4 -2596
5 -2596
6 -2596
Fixed bandwidth: 13998.93 AICc value: 5333.718
Iteration Log-Likelihood:(With bandwidth: 8663.649 )
=========================
0 -2624
1 -2502
2 -2459
3 -2447
4 -2446
5 -2446
6 -2446
7 -2446
Fixed bandwidth: 8663.649 AICc value: 5178.493
Iteration Log-Likelihood:(With bandwidth: 5366.266 )
=========================
0 -2478
1 -2319
2 -2250
3 -2225
4 -2219
5 -2219
6 -2220
7 -2220
8 -2220
9 -2220
Fixed bandwidth: 5366.266 AICc value: 5022.016
Iteration Log-Likelihood:(With bandwidth: 3328.371 )
=========================
0 -2222
1 -2002
2 -1894
3 -1838
4 -1818
5 -1814
6 -1814
Fixed bandwidth: 3328.371 AICc value: 4827.587
Iteration Log-Likelihood:(With bandwidth: 2068.882 )
=========================
0 -1837
1 -1528
2 -1357
3 -1261
4 -1222
5 -1222
Fixed bandwidth: 2068.882 AICc value: 4772.046
Iteration Log-Likelihood:(With bandwidth: 1290.476 )
=========================
0 -1403
1 -1016
2 -807.3
3 -680.2
4 -680.2
Fixed bandwidth: 1290.476 AICc value: 5809.716
Iteration Log-Likelihood:(With bandwidth: 2549.964 )
=========================
0 -2019
1 -1753
2 -1614
3 -1538
4 -1506
5 -1506
Fixed bandwidth: 2549.964 AICc value: 4764.056
Iteration Log-Likelihood:(With bandwidth: 2847.289 )
=========================
0 -2108
1 -1862
2 -1736
3 -1670
4 -1644
5 -1644
Fixed bandwidth: 2847.289 AICc value: 4791.834
Iteration Log-Likelihood:(With bandwidth: 2366.207 )
=========================
0 -1955
1 -1675
2 -1525
3 -1441
4 -1407
5 -1407
Fixed bandwidth: 2366.207 AICc value: 4755.524
Iteration Log-Likelihood:(With bandwidth: 2252.639 )
=========================
0 -1913
1 -1623
2 -1465
3 -1376
4 -1341
5 -1341
Fixed bandwidth: 2252.639 AICc value: 4759.188
Iteration Log-Likelihood:(With bandwidth: 2436.396 )
=========================
0 -1980
1 -1706
2 -1560
3 -1479
4 -1446
5 -1446
Fixed bandwidth: 2436.396 AICc value: 4756.675
Iteration Log-Likelihood:(With bandwidth: 2322.828 )
=========================
0 -1940
1 -1656
2 -1503
3 -1417
4 -1382
5 -1382
Fixed bandwidth: 2322.828 AICc value: 4756.471
Iteration Log-Likelihood:(With bandwidth: 2393.017 )
=========================
0 -1965
1 -1687
2 -1539
3 -1456
4 -1422
5 -1422
Fixed bandwidth: 2393.017 AICc value: 4755.57
Iteration Log-Likelihood:(With bandwidth: 2349.638 )
=========================
0 -1949
1 -1668
2 -1517
3 -1432
4 -1398
5 -1398
Fixed bandwidth: 2349.638 AICc value: 4755.753
Iteration Log-Likelihood:(With bandwidth: 2376.448 )
=========================
0 -1959
1 -1680
2 -1530
3 -1447
4 -1413
5 -1413
Fixed bandwidth: 2376.448 AICc value: 4755.48
Iteration Log-Likelihood:(With bandwidth: 2382.777 )
=========================
0 -1961
1 -1683
2 -1534
3 -1450
4 -1416
5 -1416
Fixed bandwidth: 2382.777 AICc value: 4755.491
Iteration Log-Likelihood:(With bandwidth: 2372.536 )
=========================
0 -1958
1 -1678
2 -1528
3 -1445
4 -1411
5 -1411
Fixed bandwidth: 2372.536 AICc value: 4755.488
Iteration Log-Likelihood:(With bandwidth: 2378.865 )
=========================
0 -1960
1 -1681
2 -1532
3 -1448
4 -1414
5 -1414
Fixed bandwidth: 2378.865 AICc value: 4755.481
Iteration Log-Likelihood:(With bandwidth: 2374.954 )
=========================
0 -1959
1 -1679
2 -1530
3 -1446
4 -1412
5 -1412
Fixed bandwidth: 2374.954 AICc value: 4755.482
Iteration Log-Likelihood:(With bandwidth: 2377.371 )
=========================
0 -1959
1 -1680
2 -1531
3 -1447
4 -1413
5 -1413
Fixed bandwidth: 2377.371 AICc value: 4755.48
Iteration Log-Likelihood:(With bandwidth: 2377.942 )
=========================
0 -1960
1 -1680
2 -1531
3 -1448
4 -1414
5 -1414
Fixed bandwidth: 2377.942 AICc value: 4755.48
Iteration Log-Likelihood:(With bandwidth: 2377.018 )
=========================
0 -1959
1 -1680
2 -1531
3 -1447
4 -1413
5 -1413
Fixed bandwidth: 2377.018 AICc value: 4755.48 Show the code
bw.fixed[1] 2377.371Show the code
gwlr.fixed <- ggwr.basic (status ~ distance_to_city +
distance_to_tertiary_road +
distance_to_town +
water_point_population +
local_population_1km +
usage_capacity +
is_urban +
water_source_clean,
data = Osun_wp_sp,
bw = bw.fixed,
family = "binomial",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE) Iteration Log-Likelihood
=========================
0 -1959
1 -1680
2 -1531
3 -1447
4 -1413
5 -1413 Show the code
gwlr.fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2023-01-17 23:27:18
Call:
ggwr.basic(formula = status ~ distance_to_city + distance_to_tertiary_road +
distance_to_town + water_point_population + local_population_1km +
usage_capacity + is_urban + water_source_clean, data = Osun_wp_sp,
bw = bw.fixed, family = "binomial", kernel = "gaussian",
adaptive = FALSE, longlat = FALSE)
Dependent (y) variable: status
Independent variables: distance_to_city distance_to_tertiary_road distance_to_town water_point_population local_population_1km usage_capacity is_urban water_source_clean
Number of data points: 4756
Used family: binomial
***********************************************************************
* Results of Generalized linear Regression *
***********************************************************************
Call:
NULL
Deviance Residuals:
Min 1Q Median 3Q Max
-129.368 -1.750 1.074 1.742 34.126
Coefficients:
Estimate Std. Error z value Pr(>|z|)
Intercept 3.540e-01 1.055e-01 3.354 0.000796
distance_to_city -1.764e-05 3.391e-06 -5.202 1.97e-07
distance_to_tertiary_road 1.001e-04 2.040e-05 4.910 9.13e-07
distance_to_town -1.544e-05 2.825e-06 -5.466 4.60e-08
water_point_population -5.098e-04 4.476e-05 -11.390 < 2e-16
local_population_1km 3.452e-04 1.779e-05 19.407 < 2e-16
usage_capacity1000 -6.206e-01 6.966e-02 -8.908 < 2e-16
is_urbanTRUE -2.667e-01 7.474e-02 -3.569 0.000358
water_source_cleanProtected Shallow Well 4.947e-01 8.496e-02 5.823 5.79e-09
water_source_cleanProtected Spring 1.279e+00 4.384e-01 2.917 0.003530
Intercept ***
distance_to_city ***
distance_to_tertiary_road ***
distance_to_town ***
water_point_population ***
local_population_1km ***
usage_capacity1000 ***
is_urbanTRUE ***
water_source_cleanProtected Shallow Well ***
water_source_cleanProtected Spring **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 6534.5 on 4755 degrees of freedom
Residual deviance: 5688.9 on 4746 degrees of freedom
AIC: 5708.9
Number of Fisher Scoring iterations: 5
AICc: 5708.923
Pseudo R-square value: 0.129406
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 2377.371
Regression points: the same locations as observations are used.
Distance metric: A distance matrix is specified for this model calibration.
************Summary of Generalized GWR coefficient estimates:**********
Min. 1st Qu. Median
Intercept -3.7021e+02 -4.3797e+00 3.5590e+00
distance_to_city -5.4555e-02 -6.5623e-04 -1.3507e-04
distance_to_tertiary_road -3.1622e-02 -4.5462e-04 9.1291e-05
distance_to_town -8.6549e-03 -5.2754e-04 -1.6785e-04
water_point_population -2.9696e-02 -2.2705e-03 -1.2277e-03
local_population_1km -7.7730e-02 4.4281e-04 1.0548e-03
usage_capacity1000 -5.5889e+01 -1.0347e+00 -4.1960e-01
is_urbanTRUE -7.3554e+02 -3.4675e+00 -1.6596e+00
water_source_cleanProtected.Shallow.Well -1.8842e+02 -4.7295e-01 6.2378e-01
water_source_cleanProtected.Spring -1.3630e+03 -5.3436e+00 2.7714e+00
3rd Qu. Max.
Intercept 1.3755e+01 2171.6373
distance_to_city 1.5921e-04 0.0162
distance_to_tertiary_road 6.3011e-04 0.0237
distance_to_town 2.4490e-04 0.0179
water_point_population 4.5879e-04 0.0765
local_population_1km 1.8479e-03 0.0333
usage_capacity1000 3.9113e-01 9.2449
is_urbanTRUE 1.0554e+00 995.1840
water_source_cleanProtected.Shallow.Well 1.9564e+00 66.8914
water_source_cleanProtected.Spring 7.0805e+00 208.3749
************************Diagnostic information*************************
Number of data points: 4756
GW Deviance: 2815.659
AIC : 4418.776
AICc : 4744.213
Pseudo R-square value: 0.5691072
***********************************************************************
Program stops at: 2023-01-17 23:27:45 Visualising Confusion Matrix
Show the code
gwr.fixed <- as.data.frame(gwlr.fixed$SDF)Show the code
gwr.fixed <- gwr.fixed %>%
mutate (most = ifelse(
gwr.fixed$yhat >= 0.5, T,F
))Show the code
Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
FALSE 1833 268
TRUE 281 2374
Accuracy : 0.8846
95% CI : (0.8751, 0.8935)
No Information Rate : 0.5555
P-Value [Acc > NIR] : <2e-16
Kappa : 0.7661
Mcnemar's Test P-Value : 0.6085
Sensitivity : 0.8671
Specificity : 0.8986
Pos Pred Value : 0.8724
Neg Pred Value : 0.8942
Prevalence : 0.4445
Detection Rate : 0.3854
Detection Prevalence : 0.4418
Balanced Accuracy : 0.8828
'Positive' Class : FALSE
Show the code
Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
select(c(ADM2_EN, ADM2_PCODE,
ADM1_EN, ADM1_PCODE,
status))Show the code
gwr_sf.fixed <- cbind(Osun_wp_sf_selected, gwr.fixed)Visualising coefficient estimates
The code chunks below is used to create an interactive point symbol map.
Show the code
tmap_mode ("view")
prob_T <- tm_shape(Osun) +
tm_polygons(alpha = 0.1) +
tm_shape (gwr_sf.fixed) +
tm_dots (col = "most",
border.col = "gray60",
border.lwd = 1) +
tm_view (set.zoom.limits = c(8,14))
prob_TWe will convert the t_score of the variable to its equivalent p-value and retrieve the statically significant rows.
We will now visualise the standard error of the distance to tertiary road after filtering by their p-value using tmap.
Show the code
tmap_mode("view")
tertiary_TV <- tm_shape(Osun)+
tm_polygons(alpha=0.1)+
tm_shape(gwr_sf.fixed[gwr_sf.fixed$distance_to_tertiary_road_TV> 1.9605 | gwr_sf.fixed$distance_to_tertiary_road_TV < -1.9605,])+
tm_dots(col="distance_to_tertiary_road_TV",
border.col="gray60",
border.lwd = 1)+
tm_view(set.zoom.limits = c(8,14))
tertiary_SE <- tm_shape(Osun)+
tm_polygons(alpha=0.1)+
tm_shape(gwr_sf.fixed[gwr_sf.fixed$distance_to_tertiary_road_TV> 1.9605 | gwr_sf.fixed$distance_to_tertiary_road_TV < -1.9605,])+
tm_dots(col="distance_to_tertiary_road_SE",
border.col="gray60",
border.lwd = 1)+
tm_view(set.zoom.limits = c(8,14))
tmap_arrange(tertiary_SE, tertiary_TV, asp=1, ncol=2, sync=TRUE)Show the code
gwr_sf.fixed[gwr_sf.fixed$distance_to_tertiary_road_TV> 1.9605,]Simple feature collection with 1 feature and 42 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 231373.6 ymin: 349636.1 xmax: 231373.6 ymax: 349636.1
Projected CRS: Minna / Nigeria Mid Belt
ADM2_EN ADM2_PCODE ADM1_EN ADM1_PCODE status Intercept distance_to_city
1238 Ife South NG030014 Osun NG030 TRUE -98.47782 -0.0001811015
distance_to_tertiary_road distance_to_town water_point_population
1238 0.003932217 0.002531213 0.007106841
local_population_1km usage_capacity1000 is_urbanTRUE
1238 -0.001787563 -1.422056 34.26977
water_source_cleanProtected.Shallow.Well
1238 6.289344
water_source_cleanProtected.Spring y yhat residual Intercept_SE
1238 -7.225437 TRUE 0.9981949 0.001805081 6385.643
distance_to_city_SE distance_to_tertiary_road_SE distance_to_town_SE
1238 0.0004576677 0.00184112 0.008159577
water_point_population_SE local_population_1km_SE usage_capacity1000_SE
1238 198.8845 0.01401122 2204.343
is_urbanTRUE_SE water_source_cleanProtected.Shallow.Well_SE
1238 4458094 13.14474
water_source_cleanProtected.Spring_SE Intercept_TV distance_to_city_TV
1238 154.9895 -0.01542175 -0.3957053
distance_to_tertiary_road_TV distance_to_town_TV water_point_population_TV
1238 2.135774 0.3102138 3.573351e-05
local_population_1km_TV usage_capacity1000_TV is_urbanTRUE_TV
1238 -0.1275808 -0.0006451157 7.687089e-06
water_source_cleanProtected.Shallow.Well_TV
1238 0.4784685
water_source_cleanProtected.Spring_TV coords.x1 coords.x2 most
1238 -0.04661889 231373.6 349636.1 TRUE
pval_distance_tertiary Geometry
1238 0.0327488 POINT (231373.6 349636.1)Show the code
pval_distance_tertiary [1] 1.00049787 0.90016494 0.99083279 0.88783432 0.99945806 1.00030565
[7] 1.00308202 0.97363787 1.00005920 0.99043059 1.52004727 1.00047901
[13] 1.00048549 0.99843143 0.99995500 0.99582917 1.00173697 0.99994920
[19] 0.99608495 0.99469904 1.00025560 0.99009833 1.02946495 1.01112284
[25] 1.86506379 0.99824092 0.99463622 0.95368946 1.00004644 1.00830149
[31] 0.87717721 1.10062424 1.00049336 0.99427489 0.99447747 1.02805425
[37] 0.99973377 1.00483363 1.55889184 1.06930536 0.99422901 1.00025132
[43] 1.00251307 0.85702139 0.88113672 0.98343875 0.96802665 0.91246078
[49] 0.99074911 1.00029071 1.07607794 0.97369576 0.98453255 0.99012906
[55] 0.99975668 1.00010115 1.00025589 1.00068643 0.99993783 1.00229459
[61] 1.00558391 1.00080016 1.31670122 0.99888749 0.99999301 1.00286789
[67] 1.02720386 1.00009721 1.02501063 0.98817397 0.97296478 1.00033132
[73] 1.00073097 0.99534014 1.00437456 0.98283964 1.06968070 0.98859041
[79] 0.99815810 0.99591193 0.99959462 0.99977590 0.99537125 0.99830446
[85] 0.99791333 0.99933707 0.99989686 0.96722910 0.99918228 1.00183421
[91] 1.24190480 0.91176292 0.99607901 0.99857715 1.00035986 0.99983974
[97] 1.02443440 1.01651630 0.99965391 1.00861113 1.28914852 1.09219022
[103] 0.99900701 1.00041194 1.00009009 0.99979779 1.01108667 0.99870538
[109] 0.96621576 1.05112955 1.00526576 0.94488983 0.99817066 1.00024652
[115] 0.99994341 0.99617283 1.00016640 1.01591444 1.00296258 1.00014862
[121] 1.00295924 0.99221471 0.99992233 0.90740650 1.00179408 0.99862779
[127] 0.99964263 0.98597181 1.00599087 1.00907856 0.99862678 0.99622023
[133] 1.00053740 1.00232389 0.88935171 1.00014561 0.92203242 1.00688206
[139] 0.57878172 1.06432991 0.99933328 0.99986696 1.49987047 1.34821504
[145] 0.99508370 1.00003033 0.99431954 0.98972711 0.99857317 1.00000538
[151] 1.00008718 1.00450195 1.00148713 0.26695977 1.00380155 0.99995601
[157] 0.99984044 0.89809991 1.00249446 1.00755759 0.98948047 0.99882419
[163] 1.01292447 1.00469571 1.01029467 1.00011124 0.30210933 0.99015477
[169] 0.98874585 0.99999207 0.99993416 0.98804919 1.01522743 0.99998786
[175] 0.99956952 0.99995238 0.99653816 1.00179222 1.19920863 1.00009692
[181] 1.00144660 1.42239131 0.99479140 1.00109988 1.00202201 0.88582071
[187] 0.80221194 0.99999183 0.99999166 0.99942748 0.99994821 1.00076060
[193] 1.00003875 1.99483849 0.99837025 1.00036251 0.99974781 0.99745391
[199] 0.99796968 0.99997316 0.89101353 0.99688644 1.00025529 1.02388416
[205] 1.01914861 1.00021819 1.00057177 0.99963966 0.99992611 1.04513282
[211] 0.99737648 0.99670616 0.99889287 0.99996241 1.00024487 0.99525168
[217] 0.99418559 1.00630364 0.73500620 1.00686007 0.99759371 0.98507388
[223] 1.00733622 0.99725001 0.99366638 1.00012672 0.99992370 0.98031449
[229] 0.99997113 1.00041633 0.99757624 1.00025131 1.29864094 0.99635356
[235] 0.99840518 0.99291148 1.00054280 0.99985206 0.81921316 1.00005670
[241] 1.01335968 0.99900538 0.98911004 1.00204562 0.99967560 0.99360374
[247] 1.00026246 0.99802313 1.00039290 1.01110595 1.00003403 0.99502549
[253] 0.98110984 1.02181566 0.99996669 0.94259818 0.99772433 1.00455291
[259] 1.00007394 0.99704421 1.00028980 1.09106313 1.00206921 1.00005656
[265] 0.99890328 1.00228415 0.99220526 0.96954830 1.03430013 1.00062585
[271] 1.00905374 0.99995652 1.00004949 0.98539275 1.00050039 0.97451013
[277] 0.99999540 1.00019914 0.99963005 0.97634435 1.16573445 0.98788726
[283] 1.00004133 1.00005550 1.00182568 1.08923389 1.15684080 1.00688811
[289] 0.99767284 0.97289088 0.99983840 0.99769478 0.99808728 0.99996952
[295] 1.00002676 0.93738004 0.99329532 1.00030431 0.98701052 1.00807580
[301] 0.99999987 0.99895975 1.12887775 0.84491331 0.99750115 1.00004750
[307] 0.98866060 1.00008462 0.97460767 0.98635564 0.90907223 1.02841736
[313] 0.99953316 0.97431525 1.00898953 1.00952033 1.00440117 0.99998951
[319] 1.00828509 1.00326135 1.00006227 1.00009769 1.00055250 1.00008940
[325] 0.99701755 0.99317113 1.03531956 1.03129793 0.99392665 1.00024932
[331] 1.00004807 0.99501891 0.98202306 1.00345636 0.99990373 0.99031675
[337] 1.00135823 0.99998024 0.99543169 1.01317439 0.98082713 1.00739255
[343] 1.00011127 0.99995194 0.87038353 1.00004020 1.01280739 0.99998914
[349] 0.99980592 1.16117108 1.00003419 0.93670821 1.99988468 1.00229369
[355] 0.99998981 1.00008524 0.99999760 0.96730052 0.99184357 1.05208005
[361] 0.99934533 1.00519081 1.01373061 0.99998935 0.99999313 1.00155238
[367] 1.00380147 0.99716357 1.09606220 1.16749873 0.97505703 1.00006965
[373] 0.99751084 0.97419648 0.99406607 1.00018035 1.00950336 0.99596593
[379] 1.00355232 0.99999110 1.00070426 0.99586970 1.00027755 0.94455668
[385] 1.00464451 0.99997526 0.99851883 1.00012186 1.02816925 0.99993926
[391] 1.00042867 1.00010312 1.00474195 1.00006173 0.98629405 1.00026676
[397] 0.84045306 1.02235053 1.01379876 1.00053231 1.00004654 1.00972560
[403] 0.99503114 1.00280095 1.00003061 0.99961861 0.99774948 1.01496005
[409] 0.99852507 0.98318017 1.02361629 0.99565681 1.07789607 0.88042513
[415] 0.99675866 1.00009027 0.99573069 0.98552258 0.99571278 1.00030390
[421] 0.99689609 0.88040110 0.99769204 0.99125565 0.75783723 0.99828348
[427] 1.00085862 0.99719898 1.08799077 1.02282255 0.99996105 1.00430431
[433] 1.00025091 1.01385038 0.98986621 1.09260545 1.02453498 0.99867610
[439] 1.01091384 0.92624299 0.99781590 0.99772266 0.99971931 0.99768436
[445] 0.99523901 1.00045099 0.99983594 0.99867919 0.99530938 1.00020106
[451] 0.99708130 1.00005632 1.02509339 0.99187540 0.98375408 0.92848040
[457] 0.97283729 1.00869810 1.00463037 0.99768482 0.92454376 0.96901515
[463] 1.01452167 1.05587957 1.00008285 1.00949199 0.98497587 0.99628104
[469] 1.02698656 0.99978161 0.99936018 1.00012069 0.99941654 0.98536923
[475] 1.00785322 0.97393577 1.00001408 1.00041806 1.05061037 1.00009709
[481] 1.27512291 0.99994206 1.00527592 0.99994813 0.99996857 0.99969241
[487] 0.98629324 0.97103767 0.99935065 1.05010525 0.99966064 0.99857300
[493] 0.99826630 1.00006668 0.99996732 0.99729468 0.99973620 1.00006130
[499] 0.99992910 1.00061112 1.00027600 1.00122571 1.00011265 0.07121212
[505] 1.01018692 0.99994703 1.00895699 0.99994878 0.99989144 0.99696195
[511] 0.99430020 1.00004061 0.99454950 0.99997430 0.88394785 1.00014088
[517] 0.99997244 1.01537597 0.99773528 0.99808190 1.00003975 0.90837507
[523] 0.98875923 0.99722011 0.99984571 0.87444358 1.00683908 1.00455317
[529] 1.00040829 0.99320041 0.99324609 0.99777520 0.99523874 0.99817481
[535] 1.57982857 0.97605784 1.00020767 1.00018496 0.99906289 0.98850716
[541] 0.99722810 0.99941137 0.99933159 1.00545609 1.00009354 0.99934571
[547] 1.04161533 1.01387609 0.99986160 1.99990185 0.99986819 0.99974215
[553] 0.81505553 1.00125200 1.00009791 0.99994950 1.00008978 0.99833918
[559] 0.99999134 0.81214687 1.00133332 1.00035678 1.00149555 1.00015443
[565] 1.00020194 1.00948356 0.99982018 1.01481097 1.00554917 0.99639449
[571] 1.00085641 0.87305517 0.98297523 1.06753696 0.99403650 0.99976029
[577] 0.90392449 1.00035831 0.99967075 1.00156417 0.99935007 0.66138089
[583] 0.99987058 1.00092402 0.99753291 0.99994224 0.99245294 1.00152647
[589] 1.00037346 0.99950462 1.00011012 0.99702715 0.99987734 1.01333011
[595] 0.99663167 1.00023058 1.09541511 1.00611875 0.99996489 1.00344132
[601] 0.68844657 0.99411174 1.00167742 0.99997134 0.99485099 0.89980952
[607] 1.00108083 0.98464108 0.99134380 0.99998695 1.00268239 1.00490890
[613] 0.99084291 0.99994553 0.99967887 1.00022112 0.99873761 1.00004292
[619] 1.00055041 1.00019662 1.01414551 1.00018190 0.93552723 0.98867266
[625] 1.01000016 1.00120731 1.00368556 1.01545312 0.98923249 0.99907337
[631] 0.99985872 0.86073476 1.00003165 1.01817799 0.99980763 1.00038377
[637] 0.98827337 0.96146027 0.99957893 1.00041594 1.00175723 1.00006160
[643] 0.99958951 0.99999645 1.00297703 1.00011517 0.98673978 1.00288909
[649] 0.99487584 0.43879931 0.99639788 1.00004177 0.99613219 0.98019194
[655] 1.00261455 1.00126995 0.99749505 1.00126325 1.00160063 1.00059368
[661] 0.99999127 1.00277762 0.98482836 1.00541113 1.99988288 1.00012847
[667] 0.99655676 0.99774189 1.00054354 1.00102552 0.99950789 0.95678169
[673] 0.99899479 1.00173870 0.82019951 0.97828880 1.00103401 1.00137825
[679] 0.99585379 1.06778406 0.99992394 1.01186239 0.99999287 0.99719743
[685] 1.01120060 0.99806670 0.99883454 1.00345543 0.99999134 1.00028637
[691] 1.00126116 0.97033899 1.00000305 1.00121022 1.00016677 0.99041175
[697] 1.00009050 1.00212478 1.06343230 0.98893902 1.00201824 0.99659111
[703] 0.84459022 1.08344183 1.07587502 0.40540495 1.00135257 1.00035227
[709] 0.73766369 1.01625805 1.00187880 1.00178142 0.84191754 0.96653724
[715] 0.99974208 1.03411201 0.99997056 0.99465411 1.00010412 1.00007543
[721] 1.05855824 1.00078275 1.02686928 1.00011022 0.97443496 1.00182425
[727] 0.99955998 0.83731885 0.93975520 0.99858676 0.99856669 0.99997966
[733] 1.02783994 1.01791422 0.96893278 0.99491911 1.00054242 1.00011608
[739] 1.00870778 1.00028240 1.03840669 1.05883954 0.99998894 1.00709471
[745] 0.99789008 0.96868069 1.00046797 1.00017264 1.00073348 1.00025059
[751] 1.00106779 0.99819533 1.00024009 0.98047643 1.00024405 1.00006860
[757] 1.01867519 0.99709057 1.01600005 0.99990446 0.97960902 1.00014844
[763] 1.00005045 0.87900518 1.01193630 0.99276130 1.00265789 1.00008994
[769] 0.99996746 0.99808637 1.01479501 0.99927707 0.99800608 0.99991157
[775] 1.00956327 0.99980636 1.02097195 1.00006988 0.99999767 0.98371654
[781] 0.99159925 0.99998285 1.00083313 1.09375113 0.99059611 1.00003234
[787] 1.00017491 0.98304496 1.01735806 0.99473869 0.97072834 1.00722327
[793] 0.99927203 1.03562666 0.99272582 1.00560014 1.00011258 0.37865829
[799] 1.00515276 0.48032901 1.03478111 0.99882910 1.00311203 1.29359054
[805] 0.99563889 0.94846520 0.96637459 0.99672782 0.98519655 1.00642947
[811] 1.00021546 1.00020747 1.00007232 0.98799490 0.99980637 0.86279093
[817] 1.02020195 1.01355440 1.00023238 0.99987262 0.99998503 1.00140791
[823] 0.99995100 0.99672903 1.12065204 0.99840135 1.00006629 1.00191171
[829] 1.00712852 0.99417235 1.00023979 0.99803534 0.99926571 0.99992565
[835] 1.00547027 1.00537840 1.03536351 1.00486639 1.00000072 1.00118410
[841] 1.02683882 0.99186116 1.00004773 0.98773182 1.00034771 0.99647731
[847] 1.27872737 1.02509213 1.01470701 0.99335953 0.99929707 0.99019748
[853] 0.97625877 0.98660352 0.99997780 0.98027102 0.98711554 1.00070169
[859] 1.00007405 1.00970843 1.00181343 1.00166802 0.89783826 1.04628895
[865] 1.01903699 0.99698739 1.00156004 1.00172556 1.00061886 0.89515373
[871] 0.99863610 1.00068021 1.00017462 1.00518884 0.99709509 0.65458688
[877] 0.99922789 0.94213160 0.99712369 1.03853895 0.99331838 1.00407523
[883] 1.01052520 0.99981246 1.00231655 1.00006279 0.82801661 0.99729296
[889] 1.06663992 0.99991146 0.99963910 0.98508250 1.01363882 1.00008956
[895] 0.95953342 1.00054697 1.00269067 0.99036119 0.99998468 1.00109131
[901] 0.99981197 0.99754007 1.00012379 0.99348525 0.99995094 0.96864405
[907] 0.99754670 0.98537280 0.97622017 1.00133616 1.00031722 1.00361084
[913] 1.00008944 1.00011772 0.99994159 1.00016331 1.00145472 0.99976629
[919] 0.99736219 0.99708093 0.99974446 1.03298275 0.99997784 0.99794336
[925] 0.99995406 0.99973787 1.00003775 0.95737738 0.99877709 1.01311049
[931] 0.99560121 0.97974838 0.97810352 0.98845004 1.00013096 1.00412366
[937] 1.00014052 0.87847168 0.99996983 0.97767865 0.99580753 1.00756928
[943] 0.99455666 1.00655965 1.00041685 1.01308777 1.00524978 0.99999820
[949] 1.00410414 1.00780016 1.00440053 1.01066471 0.98685093 0.99350190
[955] 1.00080504 0.99949736 1.00904907 0.99559943 1.01782092 0.99997792
[961] 0.99375320 1.00507627 0.91431906 0.96902311 1.00099196 1.00644476
[967] 0.99877894 0.99764176 1.00012982 0.99727446 1.15616366 1.04240191
[973] 0.99446024 0.99999781 1.00011826 1.00009127 1.00002587 1.00026415
[979] 1.00015886 1.00187970 1.00122114 1.02445064 0.99969432 0.99778129
[985] 1.00194556 0.99996843 1.00362712 1.00015776 0.99758949 1.00007151
[991] 1.00002875 0.99724851 0.99994310 1.00020247 0.98956315 1.00006385
[997] 0.99837965 0.99999244 1.00011093 0.25593602 1.00052503 1.00054129
[1003] 0.98796841 0.43842604 0.99998248 1.00052033 1.00009123 0.99999870
[1009] 1.00735747 1.00005600 0.80651007 1.05691004 0.97950499 0.99986343
[1015] 1.00418026 1.00005917 1.00002649 0.91206748 0.99646308 1.00231776
[1021] 0.99999178 1.00042652 1.00008076 0.99978656 1.07201856 0.96412683
[1027] 0.99518300 0.99769365 0.99786374 1.03724198 0.99443514 0.99997255
[1033] 1.00721022 0.99265914 0.99932050 0.99912099 1.11237510 0.99927675
[1039] 1.00010153 1.00006389 1.01461719 0.98201669 1.00008773 0.99399573
[1045] 1.01020298 0.99999162 1.28399669 1.00176794 0.98842266 1.00003126
[1051] 1.00018391 0.99980070 0.28899839 0.87428653 1.00031506 1.00151667
[1057] 1.00008363 1.00011511 1.00549523 1.04977795 1.00555912 1.07917464
[1063] 1.00714020 0.99992027 1.01640135 0.99989611 0.99937136 0.99793709
[1069] 0.99963073 1.00378081 1.04690859 0.91508066 0.88909106 1.01375161
[1075] 1.00117228 0.99689792 0.94814674 0.99970817 0.99993686 0.91582704
[1081] 1.08942072 1.01268933 0.99262074 1.01691636 1.00335456 1.02071873
[1087] 0.99992900 1.00039740 0.99971827 0.98947777 1.00429864 1.00023176
[1093] 1.00599498 1.00150805 1.01366467 0.99985707 1.06941979 0.34837214
[1099] 1.00032371 1.00012714 0.99724379 0.99711799 0.99999378 1.00443931
[1105] 1.00041471 1.00620868 1.12407964 1.05127721 1.00062615 1.00518330
[1111] 0.97366143 1.00014354 0.99789036 0.06422510 1.04000837 0.99036482
[1117] 0.99947148 0.99080597 1.01028205 1.00014092 1.02144991 0.99423504
[1123] 1.00005805 0.99769405 0.99939297 0.99971614 0.99979798 0.98664696
[1129] 0.99471325 1.01039858 0.91485525 1.00008882 0.98329834 1.01026294
[1135] 1.00474647 1.00372440 1.00095858 0.99995219 0.99998971 1.03812480
[1141] 0.99822036 1.00007255 1.10422614 1.00002859 0.99984936 1.00155983
[1147] 1.00076484 0.99985648 0.99582539 0.99833267 0.99971166 1.01373919
[1153] 0.99994722 1.00019236 0.98840824 1.00453643 1.00139316 0.98700552
[1159] 1.07631728 0.99323003 0.99707409 1.00777285 0.99865459 1.03004212
[1165] 1.33391880 1.00006574 0.99696920 0.99857776 1.01132642 1.00969882
[1171] 1.00247173 1.12081982 0.95711288 1.00081767 0.93200196 0.99482092
[1177] 0.99884556 0.99551390 0.97988907 1.00498697 1.37531737 0.99996473
[1183] 0.99871915 0.93740398 0.99618957 1.00003217 0.99686750 0.99718837
[1189] 0.97806027 1.00123508 0.96936873 1.00053864 1.00080561 1.00047386
[1195] 0.98808977 0.99947951 1.01674567 1.01482284 1.20097442 1.00016694
[1201] 0.99670321 1.00417187 0.99414589 0.99998393 0.99999215 1.00020808
[1207] 1.00079754 1.00259022 1.00439391 0.93547167 1.00009030 0.99925322
[1213] 0.98645367 0.99999779 1.00016540 1.00057457 1.00031490 1.00343022
[1219] 1.00021792 0.99661464 0.99998267 1.00441951 1.01442728 1.00034296
[1225] 0.98764330 0.23378141 0.98150513 0.99358963 0.98109977 0.99965340
[1231] 0.84166047 0.99257860 1.09109913 0.99807096 0.99904580 1.00017395
[1237] 1.00007012 0.03274880 1.01693064 0.99713711 0.87205199 0.99455342
[1243] 0.99155367 1.02115934 1.00196966 1.00007183 1.00015707 1.00160529
[1249] 1.01012641 0.99987096 0.99510404 1.00723686 1.00013149 0.90282183
[1255] 1.00011906 1.06631189 1.00216650 1.00031508 1.00174662 0.77528457
[1261] 0.98722106 1.00004731 0.99763444 0.95939762 0.99709103 0.99550171
[1267] 1.00577726 0.95602973 0.99261410 1.06928643 0.97386119 0.99824299
[1273] 1.38086531 1.00028020 1.00003403 0.65112162 1.01025962 0.99458411
[1279] 1.00409545 0.99959227 0.99966240 1.00219752 1.01415528 0.92831541
[1285] 1.00192633 1.01325116 1.40892222 0.99875253 0.97367732 0.94714238
[1291] 1.00098747 1.01904990 0.98974256 1.00119599 1.00006846 0.99992406
[1297] 0.96654575 0.98725521 1.00511296 1.99544652 1.01511944 1.00003070
[1303] 0.99693203 0.99304299 0.96503964 0.99500777 0.99970691 1.00009117
[1309] 0.98182912 1.00041243 1.99579948 0.99848990 0.99975881 0.88465777
[1315] 1.00020526 1.22090947 0.98854348 1.00028967 1.00006468 1.00005214
[1321] 1.00043528 0.99999176 0.99804280 1.00339372 1.00990016 0.99984063
[1327] 1.00028103 0.99959101 0.99577723 0.99992027 0.99752774 0.99740563
[1333] 0.99990551 0.99933764 0.98135125 1.00045852 0.99934937 1.00058355
[1339] 0.99532259 0.99794643 0.99730666 1.00009054 0.99652602 1.07032573
[1345] 1.00007873 0.90117000 0.99221843 0.99429960 1.00020935 1.00149304
[1351] 1.01365354 0.99963346 0.99942946 1.00038450 1.00000198 0.99682848
[1357] 1.04814895 0.99976463 0.95042502 0.99882490 1.00399279 1.14069651
[1363] 0.99798190 0.99397479 0.99942832 1.06422602 0.99984754 1.00075866
[1369] 0.99612667 1.01473456 0.99998526 0.99821689 0.43164434 0.99943142
[1375] 0.99995184 0.99289521 0.84375941 1.00347157 1.00015605 0.99609374
[1381] 0.96733798 1.00178572 0.99554406 1.08750157 0.99989454 0.99992037
[1387] 0.96836270 0.99764710 0.99994532 0.99988171 0.99903366 1.01756968
[1393] 0.93103631 1.00043927 1.00036702 0.99801160 1.00347292 0.99297510
[1399] 1.00818984 0.98352757 0.98463323 0.99987201 0.99510553 0.99970483
[1405] 0.82613650 0.99665618 0.99317029 0.99829011 0.99712798 1.02823730
[1411] 0.99993872 0.99993789 0.99401912 1.00404059 1.00103739 1.00062512
[1417] 1.01466023 0.99970619 0.90366537 0.97844544 1.00021932 1.01751155
[1423] 1.00016182 1.00006140 0.99957971 1.07219072 1.00028369 0.99601021
[1429] 1.04395015 1.00012210 0.82528645 0.99990358 0.99985799 0.99501322
[1435] 0.99994378 1.00025236 0.57171681 1.03149710 0.99291412 1.05479039
[1441] 0.99670128 1.00390991 0.99977175 0.99960530 1.00702801 1.00013535
[1447] 1.00248181 0.62387189 1.08515031 1.00018132 1.00007894 0.59172345
[1453] 1.00029156 1.00000158 1.01323507 0.99119882 1.00356836 0.99866035
[1459] 1.00010084 1.00084727 1.00024698 0.85279203 1.00239145 0.99927842
[1465] 0.99980242 1.41224357 0.98956814 0.98580104 0.99987630 0.99985074
[1471] 0.99998190 1.00555757 0.89964190 0.91473517 0.98779397 0.99996787
[1477] 1.00131090 0.99868481 0.99117416 0.99987893 0.99984404 1.06823554
[1483] 0.99586245 0.99975246 1.00011910 1.10320223 1.00047986 0.99952629
[1489] 1.00029873 0.93065394 1.00032112 1.00212660 1.00530298 0.99988050
[1495] 0.98970047 0.99749288 0.99596510 1.00096391 1.01644278 0.98416031
[1501] 1.00313430 0.99405772 0.99994455 0.99987828 1.00047698 0.99408986
[1507] 0.99301493 1.00379045 0.99657807 1.02195830 1.00008256 0.99779121
[1513] 1.00156137 1.01777432 1.16398639 1.00601825 0.99470262 0.98811034
[1519] 1.00373154 1.99574106 0.99661198 1.00016833 1.00009736 0.99850470
[1525] 1.00096098 0.65125147 0.99949067 0.78709898 1.00741534 1.00646259
[1531] 0.89285088 1.09182439 1.00536460 0.99942203 0.96948475 1.00833609
[1537] 0.99992868 1.01883325 0.99439255 1.00037014 0.98310091 0.99999619
[1543] 1.00005900 0.99981853 0.89051964 0.99460953 0.99914519 1.00010106
[1549] 0.97773908 0.99794481 0.99996875 1.00248944 1.00093107 1.99419107
[1555] 0.99933326 0.81160911 1.00087655 1.00012967 0.99787554 0.99986055
[1561] 0.99985650 0.99113101 0.99996886 1.00066151 1.00005328 0.99507407
[1567] 1.00082838 0.99269078 1.00452773 0.99996138 0.99836361 1.02141981
[1573] 1.00006031 0.97055766 0.97663477 0.99592465 0.99842511 0.99032009
[1579] 1.00009995 0.99432099 0.99807472 0.98326757 1.00107425 1.00134438
[1585] 0.97977671 1.00188182 1.00002995 1.00513399 0.98882874 1.00017558
[1591] 0.99807184 1.00013257 0.98224783 0.96432877 1.00052792 0.99944781
[1597] 1.00029512 0.99462820 1.00095644 0.98756388 0.98758162 1.00114844
[1603] 0.99830956 1.01447072 0.95495307 0.99141734 0.99978357 0.99967079
[1609] 0.99982690 1.00053301 1.00003491 0.96743938 1.00199350 1.00004729
[1615] 1.01879643 1.00636125 1.02102280 0.99938388 0.99996772 0.99403457
[1621] 0.99996951 1.25782740 0.99875432 1.00484617 0.98867459 1.00698644
[1627] 1.00012910 1.01909617 0.99843612 1.00034425 1.00009107 0.98371692
[1633] 0.99993528 1.03459179 1.01536913 1.00014973 0.99513786 0.99875032
[1639] 1.00028871 0.99984777 0.99993238 0.99650325 0.25051919 0.99713822
[1645] 0.84597141 1.02036697 0.99285657 1.00380236 0.99526067 0.99992006
[1651] 1.00442360 1.00002214 1.00385479 1.00277676 0.98952874 0.99987936
[1657] 1.00103400 0.99997055 0.99254179 1.22263381 0.99968819 1.00442661
[1663] 0.99953128 0.99985794 0.99995960 0.99961929 1.00610404 1.00374859
[1669] 1.00359699 0.99966200 0.99800809 1.00014950 1.00002660 0.99987070
[1675] 0.94855740 1.00302146 0.99794923 1.00486855 0.99853215 1.00119408
[1681] 0.99492415 0.99450704 0.99818561 0.95849429 1.00086422 0.90951499
[1687] 0.99932227 1.00268854 0.96986766 0.99388224 0.99386324 1.00014492
[1693] 0.96846984 0.99896875 0.98792353 1.00020946 0.99640815 0.99831425
[1699] 0.99914692 0.99453117 0.99929182 1.01147194 0.99994716 0.83683327
[1705] 0.99707506 1.00010859 0.73361544 1.00007287 0.99783591 0.99994974
[1711] 1.00292785 1.04081477 0.51012040 1.00009665 0.99979247 0.99823129
[1717] 0.99648423 0.92198024 0.99991125 0.99126318 1.00019859 0.99687087
[1723] 1.00013475 0.89971961 0.99773823 1.00761985 0.98337203 0.99953570
[1729] 1.00386553 0.96516263 1.00002597 0.99967584 0.99980462 1.00018307
[1735] 0.99766341 1.00271717 1.01451405 0.99979781 0.94065887 1.01136317
[1741] 0.99983736 0.43910995 0.98760053 1.11669815 0.89386730 0.99986555
[1747] 1.00149770 1.00372328 1.00012870 0.99765978 1.00001468 0.99996547
[1753] 1.18758886 0.99908080 1.00040431 0.99086005 0.99858276 1.00006446
[1759] 1.01897603 0.99955742 0.99420317 0.99982849 0.99689232 1.00010060
[1765] 0.89216214 0.99988440 0.99968426 0.99574950 0.91278455 1.00007706
[1771] 1.00507277 0.96632251 0.99428699 1.00044306 1.00740790 1.00108544
[1777] 0.99506047 0.99878001 1.00006277 0.99994330 0.99607530 1.02030719
[1783] 0.99900939 0.99968840 0.99996206 1.00032751 0.99861617 1.00333736
[1789] 0.99979860 0.95265973 0.98887602 1.01589658 1.53837770 0.99992461
[1795] 1.00005603 0.99584095 1.00639031 0.99020322 1.00032576 0.99966136
[1801] 0.99835378 0.99997515 0.99986601 1.00008424 0.99562306 1.23734256
[1807] 0.99977431 0.99983187 0.99783605 1.10565512 1.00008419 0.99997440
[1813] 1.25804995 1.03147785 0.96525358 1.00003233 0.80904164 0.99938839
[1819] 0.99992696 0.99399977 0.99571052 1.01879100 0.99941748 1.00196143
[1825] 0.99814719 0.99576652 0.99995275 1.00038905 1.00030169 1.00018667
[1831] 1.00145107 1.00021959 1.00004682 0.99897716 0.99463052 0.99651791
[1837] 0.99757005 1.00102132 0.99819198 0.99225010 0.99827138 1.00007220
[1843] 0.99983496 0.99195219 1.00128801 0.98120199 0.99982421 0.99541116
[1849] 1.00072972 0.99954956 1.00011185 0.99810508 0.99049092 0.99999927
[1855] 1.00006121 1.00611425 0.99969785 0.99873855 0.99986665 1.00015256
[1861] 1.03322732 0.99656479 1.00407977 0.97314381 1.00021140 1.00676807
[1867] 1.00899950 0.87932368 0.99899051 1.01590219 1.00021346 1.21892814
[1873] 0.99126254 0.98851797 0.99865708 0.99286082 1.00968567 1.01975730
[1879] 0.99722568 0.99740183 1.01583554 1.03863997 1.01329528 0.99833016
[1885] 0.99650324 1.00026478 0.83534423 0.99998061 0.99934363 0.99967275
[1891] 1.00028199 0.99298882 1.00129911 1.00051003 1.00009758 1.02082376
[1897] 1.00008219 0.99313234 0.84219922 1.00010713 1.03208751 1.23743150
[1903] 0.94923850 1.00009555 1.00997047 1.00018414 1.00188848 0.99965412
[1909] 0.99706865 1.00563746 0.99742433 0.99994600 1.00563221 1.00806742
[1915] 1.00756111 0.99956555 1.00009251 1.00003398 1.00050922 0.87883017
[1921] 0.98329337 0.99984526 1.00078169 0.99750363 0.99694579 0.99787245
[1927] 1.00004221 0.99971764 0.99661206 0.64087477 0.99998307 0.99749187
[1933] 0.99968857 0.99386620 1.00002181 0.99984968 1.00067957 0.99852663
[1939] 0.99989625 0.98364599 0.99886315 0.97018617 0.99973704 1.00093800
[1945] 0.99794821 0.99498593 0.99786570 0.95498538 1.00180032 1.00048568
[1951] 1.00013564 1.00011555 0.87423140 0.99803647 1.02218484 0.99692998
[1957] 1.00009261 1.00233867 1.00004911 1.00070485 1.00178441 0.99889104
[1963] 0.99998153 0.99662963 0.99621913 0.99965330 0.98887458 0.99987254
[1969] 1.00200638 0.93488962 0.99429122 0.99553570 0.95408514 0.99081149
[1975] 0.99996898 1.00012246 1.03471750 1.62189892 0.98793636 1.02315253
[1981] 0.99986485 0.99988402 1.16233558 0.99969519 0.96822549 0.99839047
[1987] 0.66734440 0.92614678 1.00006144 0.89398484 0.99761511 1.00071853
[1993] 1.00028153 0.99809821 0.94335112 1.00027340 1.01582544 1.00838129
[1999] 0.99997005 0.99964015 1.01891964 0.99401491 0.99751161 0.99627992
[2005] 1.00266407 1.00173473 1.00012010 1.00006663 1.21307041 1.00018003
[2011] 0.99956458 1.00005474 0.80352595 0.99974076 0.99989191 0.99506407
[2017] 0.99378305 0.99964306 0.99964989 1.00010811 0.98404495 0.98736348
[2023] 0.99795018 0.89105534 0.96963436 1.00009109 1.00088514 0.99853763
[2029] 1.00017751 0.93080704 1.00061736 0.99997363 1.00016418 0.95134832
[2035] 1.00008986 0.99946445 0.99902381 0.99996067 0.99358603 1.01189570
[2041] 0.99601987 0.99462906 1.00241948 0.99785131 1.00079737 0.99989690
[2047] 0.99638726 0.99932397 0.99782996 1.00078670 1.00294746 1.00011730
[2053] 0.99957275 0.94332203 1.00006383 1.00149711 0.99519835 1.00051638
[2059] 0.99964748 1.00016697 1.01088858 1.00127463 0.97292047 0.99983980
[2065] 1.00006244 0.99759145 1.00004307 1.00066291 1.01481578 1.00071258
[2071] 1.00032283 1.00172180 0.99981812 1.00010132 0.99084954 1.01359191
[2077] 1.00134219 0.99990688 0.89949970 0.96289565 1.11833146 1.00190658
[2083] 1.01045814 0.97511812 1.00009500 0.97575578 0.99276224 1.00009857
[2089] 1.00186724 1.00102145 1.00010822 0.99033352 1.00005491 1.00009635
[2095] 0.99257595 0.99987016 1.00010038 1.00094349 1.01053793 1.00672987
[2101] 1.00099729 1.00046471 0.99935841 0.99699496 0.99518198 0.99983967
[2107] 0.99254217 0.99999435 1.02292404 1.00003523 1.00062840 0.99886999
[2113] 0.60048548 0.99934768 0.99984996 0.99944438 0.99994627 0.99366843
[2119] 0.68872438 1.00009807 0.99988464 0.99805106 1.00257164 0.99647187
[2125] 0.98579488 1.00000139 0.99927445 1.00069033 0.99929189 1.00024865
[2131] 0.99935188 0.99996833 0.96366308 1.02541338 0.99997694 0.99959374
[2137] 1.00651732 0.99915185 1.04367206 1.00074472 1.03785382 1.00061336
[2143] 0.92146898 0.99908140 1.00034348 0.98168684 1.00032136 0.71400807
[2149] 0.98665089 0.96890185 1.00278396 1.00272044 0.99977093 1.00089012
[2155] 1.00119420 0.99989861 1.00516824 1.01349675 1.00080937 1.00180792
[2161] 0.97684974 1.00006748 0.99787619 1.00013852 1.00016196 0.99810340
[2167] 0.95259376 0.99990833 1.00148473 1.00181368 0.93694575 1.01648919
[2173] 0.99874860 1.23093068 0.97294471 1.00073492 0.99993640 1.00004842
[2179] 0.99938080 1.00044356 1.00173542 0.99886343 1.00015674 0.99984204
[2185] 0.99998843 0.99478717 1.00020886 1.00675259 0.96580519 0.99779189
[2191] 0.92301100 1.02043016 0.95437591 0.99017799 0.99995981 1.02899510
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[3325] 0.40560583 1.00866348 0.99914503 1.03832163 0.99944743 1.00298087
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[3385] 0.99532218 0.98959844 1.02485002 0.41085470 1.00036362 0.99399005
[3391] 1.00100209 1.00012679 0.99993274 0.98888307 0.83595308 1.00008611
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[3433] 1.00057414 0.99591379 1.00052618 1.05648555 1.00614728 0.99297444
[3439] 0.99993433 1.00092610 0.98791941 1.18444297 0.99972088 0.99965237
[3445] 1.01501552 0.99219919 0.99996308 0.99960841 0.83184285 1.02452650
[3451] 0.99779107 0.99341924 1.00327597 0.99922339 0.99226338 0.99828753
[3457] 1.00569319 1.23448296 1.00007395 1.00010598 1.08321657 0.99839611
[3463] 1.11560074 1.00047421 0.99722483 1.00668231 0.99978179 0.99758921
[3469] 0.97856513 1.12852437 0.99972556 1.03292952 0.96290709 0.59482710
[3475] 0.86904324 0.99971026 0.99954988 0.99502574 1.14526302 0.99526822
[3481] 1.00007323 1.08128795 1.00074515 0.96688906 0.99991412 1.00012406
[3487] 1.00004107 0.99994731 1.08320786 1.00114486 0.99734573 1.00009844
[3493] 0.99965079 1.00008379 0.99994029 0.99990560 0.96448189 1.00221123
[3499] 0.98474763 1.06752508 0.39793635 0.99953337 1.00554568 0.99996589
[3505] 1.00078909 0.93258860 1.00506340 1.00714591 0.99512638 1.00196990
[3511] 0.99646730 0.99996044 1.11143482 0.99828438 0.97614524 1.00081398
[3517] 0.99956690 0.97568722 1.00518179 0.99681473 1.00020275 0.99696807
[3523] 1.00000129 0.99998382 1.00006247 0.99926113 1.09389148 0.98467792
[3529] 0.90461013 0.99899358 1.00671493 1.00001637 1.00583499 1.06622065
[3535] 0.99999149 0.99799032 1.03262756 0.99279884 0.99956259 0.89697008
[3541] 1.00037146 0.91823238 0.99944773 1.00161298 1.00025787 1.06940713
[3547] 0.99983827 0.99962594 0.99999704 1.08198769 1.00071148 1.00985801
[3553] 1.00008605 0.99990172 1.01124923 0.99955418 0.99744600 0.99999387
[3559] 1.03426519 1.02538210 1.00000192 0.99998582 1.00086101 0.98367164
[3565] 0.99921085 0.99613540 0.99982583 0.99457195 0.99942832 0.99115412
[3571] 0.92695041 0.99707520 0.99654882 1.00005000 0.99774374 0.99946072
[3577] 1.00001686 0.85614410 1.02573877 1.00015093 1.08354878 1.00003682
[3583] 0.99991179 1.00309378 0.99830110 0.99777972 1.00019758 0.80323084
[3589] 1.00380819 0.94409251 1.00722378 1.00147002 1.02849611 0.99911699
[3595] 0.99975877 1.00332079 0.99679154 0.99999526 0.99838456 0.83649292
[3601] 1.00173114 1.00202941 0.99993105 1.00246260 1.00011872 0.99414408
[3607] 0.75247920 0.99998536 0.99491673 0.93023837 0.99768869 1.00021796
[3613] 1.00017997 0.98125651 1.00672596 1.00858989 0.93133468 0.99984785
[3619] 0.99889722 1.04234956 1.00009565 1.00020389 1.00012230 0.99875387
[3625] 0.99522737 0.99571773 0.83969769 1.00221949 0.99986850 0.99212097
[3631] 1.05349212 0.99998955 0.83243504 1.00004597 1.00231845 1.00050297
[3637] 1.00112515 0.99997440 0.99975333 1.00253975 0.62713550 1.00079610
[3643] 0.99484503 1.00005509 1.00167018 1.00042471 1.00551461 0.99987096
[3649] 0.99964255 0.99682483 1.00003503 1.00009430 1.00147473 1.04385288
[3655] 0.99213145 0.99997682 0.95761935 0.99665999 0.99753936 1.00288303
[3661] 0.99248944 1.00145725 1.19837582 0.99955298 0.99813189 1.00008991
[3667] 1.00008892 1.00009728 1.00158296 1.00009974 1.03985115 1.01287979
[3673] 0.99665766 0.99664624 0.87795746 0.99932628 0.91998008 0.93270806
[3679] 0.99926262 1.00177818 1.00035494 0.93189280 0.99970381 1.00087037
[3685] 0.70418424 0.99971304 1.00255217 0.99930844 0.99990572 0.99666300
[3691] 0.99495176 1.00270184 0.99236650 1.00223253 1.00010474 0.97381825
[3697] 0.91282585 0.62745697 1.00609474 0.98912434 1.00172078 0.95683896
[3703] 0.99888183 0.88017731 0.99997344 1.01849750 1.00996514 0.99567032
[3709] 1.00270469 0.99283925 1.00010815 0.98043714 0.99121822 1.01812190
[3715] 1.00673638 0.99999237 0.99781843 0.99738849 0.99999777 0.99670676
[3721] 1.00018392 1.00220738 1.00015421 1.00014422 0.99942427 1.75629865
[3727] 0.98656238 1.00080974 0.96288221 1.00332920 1.00233694 1.00012456
[3733] 0.64945531 0.98758751 1.00005876 0.99718058 0.98836392 1.00010083
[3739] 0.99985612 0.99886474 1.00004700 1.01048168 1.02710496 0.99979839
[3745] 1.00143649 0.99944911 1.00053044 1.00003638 0.99855750 1.00045414
[3751] 1.00007497 0.99940731 1.00208859 0.99174204 0.99993152 0.85420513
[3757] 0.99963689 0.99994912 1.00114708 0.95463273 1.00913052 0.99342630
[3763] 0.99988084 1.00000148 1.04527418 1.00019719 0.97511229 0.99964843
[3769] 1.00009972 0.99997301 0.99141158 1.00034722 1.00389354 0.90467035
[3775] 1.00425339 1.00361118 1.00000108 0.99994262 0.99789914 1.02855551
[3781] 0.61579302 0.99960375 1.00024401 1.01595022 0.99931362 0.99856077
[3787] 0.99980567 0.99609297 1.00095214 1.00038187 1.02685383 0.99943067
[3793] 0.99808867 0.99996005 0.99482052 0.99768164 1.00331344 1.00030607
[3799] 0.99938248 1.00006079 1.00325377 1.00253789 0.99959045 0.99855782
[3805] 1.03462121 0.99555326 0.99992208 0.99183416 0.99418894 0.99784082
[3811] 1.00039557 1.00014331 0.99022491 0.99804775 0.99999630 0.99804801
[3817] 0.99330875 1.00062647 0.99462058 1.02704414 0.99995421 0.99336068
[3823] 1.00008502 1.00680597 1.00015989 0.99998033 1.10230300 0.98595232
[3829] 0.99990823 0.80460987 0.99970206 0.99989094 1.00088149 0.93305459
[3835] 0.99978620 1.02831365 1.00008379 1.00000885 0.96621451 0.99986713
[3841] 0.99934520 1.02014955 1.00003008 1.00079480 1.00006044 0.99998923
[3847] 0.65014369 0.99389597 0.99786817 1.00008959 1.00008382 1.00012956
[3853] 1.00004605 1.03216657 0.61932774 1.00089568 0.99716359 0.99283559
[3859] 1.00041402 0.94006840 0.96526781 0.99688920 1.04516164 0.99665507
[3865] 0.99869388 1.00002564 1.00019658 1.01617379 0.99815326 1.01216343
[3871] 0.92703632 0.98400391 0.99977413 1.00011565 1.03889108 0.99987863
[3877] 0.99966192 0.92577717 1.14653270 0.99995369 1.00041401 0.99985828
[3883] 0.90809341 0.99996008 0.89792617 1.00003866 1.00467893 0.99990805
[3889] 0.99569361 1.00405509 0.99999328 0.99825442 0.97520398 1.00038712
[3895] 1.00192567 1.00189967 1.00020668 0.99983371 0.85521319 1.00253059
[3901] 0.99997683 1.01802546 1.00009212 1.02489124 1.00000104 0.92520882
[3907] 0.97991536 0.99690940 0.99516279 0.99611360 0.99832479 1.00199781
[3913] 0.99791886 1.00000740 0.99805018 0.99664179 1.03178101 0.99501489
[3919] 1.00008044 0.99418979 0.98810967 0.98959796 0.97887152 1.00040307
[3925] 0.81461311 0.98079172 1.00005997 0.99977549 1.00080589 0.89875649
[3931] 1.00004248 0.99994385 0.88522639 0.99188517 1.00129686 1.00006377
[3937] 0.99946831 0.98662982 0.99897864 1.00968593 1.00165298 0.99293885
[3943] 1.00060969 0.99150673 1.00576551 0.90552241 1.00006886 1.00021007
[3949] 1.00284593 1.00113030 0.98916400 0.71906744 0.93781199 1.00116499
[3955] 0.96888155 0.99677676 0.99993653 1.00035116 1.00001303 0.99942051
[3961] 1.00701509 1.00002497 1.00009894 0.99670285 1.03605033 0.99467573
[3967] 0.98488121 0.98592651 0.99783641 0.98977454 0.99983160 1.01665615
[3973] 1.00104217 0.99955669 1.01636740 0.95699850 0.99527097 0.91505742
[3979] 1.00397431 0.93807204 0.99449562 0.99898930 1.27771559 1.00178860
[3985] 1.29353743 1.00041536 1.00123783 0.99994663 1.00069199 0.99436819
[3991] 0.99543473 1.00008318 0.99992095 1.00035564 0.99998978 0.98383683
[3997] 1.00088055 0.99994632 1.04540474 0.92621145 0.99995899 1.00006891
[4003] 0.99969096 1.00000956 0.99995935 1.00078987 0.91296817 1.00005516
[4009] 0.99965587 0.99987944 1.00001142 0.99997974 0.98309101 0.99999372
[4015] 0.99600311 0.99559198 0.99607281 1.00737099 1.00124036 0.99497007
[4021] 0.99936492 1.00009716 1.00949220 1.00007602 1.00069380 1.00002698
[4027] 0.90130285 0.99829093 0.99719913 0.98920416 0.99759267 1.02873251
[4033] 0.99703540 1.00036772 0.99998711 0.99615590 0.99671418 0.99801496
[4039] 0.99857668 0.99141741 0.99859481 1.00032486 0.99933409 0.99323773
[4045] 0.99992991 0.99973793 0.92388274 0.99783941 1.00009846 1.00008219
[4051] 1.04227304 1.00577609 0.99708323 1.00107087 0.99985004 1.00015738
[4057] 1.00112373 0.91483865 1.01123192 1.00145061 1.01020902 0.99976256
[4063] 0.94202569 0.99121551 0.99171781 1.00059917 0.99996642 1.00484885
[4069] 0.97853846 1.00069236 1.00810573 0.57354283 1.00076714 1.04100100
[4075] 0.99121764 0.88170741 0.98638673 0.99998876 1.00027306 0.99990206
[4081] 0.99817247 1.27775211 1.04187115 0.98014942 1.07350226 0.99979571
[4087] 0.91646361 0.99460603 0.99634108 1.05635464 0.99598770 1.00009141
[4093] 1.01865718 0.99844571 0.99707140 1.64437368 0.99277762 1.00001239
[4099] 1.00235494 1.17501349 0.99998159 0.97598239 1.00000167 0.91493703
[4105] 0.91131790 0.99726392 1.01249846 0.99907472 1.00146884 1.00003690
[4111] 0.99983103 1.00110019 1.00006929 1.00158446 0.99945838 0.99662295
[4117] 1.05244955 0.99482075 1.00009318 1.00211336 1.11646127 0.99530754
[4123] 1.00069942 0.90288263 0.98688113 0.99250266 1.00937705 0.99197334
[4129] 1.02217274 1.00032572 1.01759917 1.00293759 1.00099837 0.99613687
[4135] 0.99576964 0.99456337 0.99857079 1.01005175 0.99967881 0.99768504
[4141] 0.96311218 0.99975237 0.99986029 0.91745897 1.00006053 0.99735525
[4147] 0.99999303 1.00686866 0.99978138 1.00511769 0.96767455 0.99982547
[4153] 1.00005767 1.00553637 0.99459077 0.39824677 1.00006329 1.00005608
[4159] 1.00011809 0.92707664 0.98515755 1.00475361 1.00097248 0.99998564
[4165] 0.98423327 1.00005645 1.00000187 1.00150741 0.87106190 0.99987505
[4171] 1.00007486 0.84115655 1.00002962 0.99701184 0.99998239 1.00040570
[4177] 0.90764079 0.99986404 1.00664691 0.84120151 0.98383153 0.99863368
[4183] 1.00065271 1.00024303 1.00005740 1.00051527 0.97910890 1.01222474
[4189] 0.98186527 1.01005369 0.96397310 0.99804939 0.99958232 0.90764767
[4195] 0.83124292 1.00010080 0.96216142 1.00003577 1.01778795 0.99683854
[4201] 0.99969492 1.00099444 1.01049019 0.99762579 1.00005744 1.00004006
[4207] 0.96548033 1.00010845 0.99999407 0.99744193 0.98508852 0.84197813
[4213] 0.99972046 0.99272629 1.00006955 0.99997800 0.99113639 1.00070823
[4219] 1.00095848 0.99008837 0.94204936 1.06322415 0.90109882 1.77950095
[4225] 0.98857984 0.99327287 0.99986569 0.99466616 0.99366483 1.00423342
[4231] 0.98512955 0.99445818 1.24156318 0.98790932 0.99743143 0.90768901
[4237] 0.73201548 1.00160885 0.99955280 1.00005707 0.99504430 0.99800311
[4243] 0.97043951 0.99916029 1.11942191 1.00127616 0.89092129 0.92525414
[4249] 0.99739516 0.99892277 0.99662023 0.94255208 0.99856294 0.99817974
[4255] 1.00015157 0.99103222 0.99996219 0.99351603 1.00001145 1.00033464
[4261] 1.02720999 0.99873011 1.00188374 0.99944243 0.99998124 0.96760724
[4267] 0.68976489 0.99578296 0.98081555 0.99928616 1.00002541 0.87988462
[4273] 1.03905792 0.98712234 1.01213731 0.99998215 0.99797067 0.99932121
[4279] 0.99998925 0.98960191 0.87008178 1.00006047 0.89019035 1.00086500
[4285] 0.71322223 0.90477897 0.99781474 1.00440539 0.98965329 1.04918865
[4291] 1.00228328 0.98244793 1.04524967 0.99714227 0.99999298 0.99834505
[4297] 1.03364134 0.86871383 0.99993057 0.99994693 1.02386430 0.95684525
[4303] 0.99470155 1.01570940 0.99994807 1.00169773 0.97743258 0.32033308
[4309] 0.99997840 1.00008099 0.99974259 0.91442856 0.99932030 0.99998919
[4315] 0.99924681 1.00575649 1.00021772 1.00085291 0.99978766 0.99851802
[4321] 1.00004648 1.00217626 0.99320441 1.00005310 1.00160294 1.04127637
[4327] 0.81444166 1.03928409 1.02930039 1.00029782 1.00499210 1.00003295
[4333] 0.97616982 0.99582227 0.99071191 1.00005212 0.99994347 1.00002847
[4339] 1.04330812 1.00270404 0.99657827 1.00254529 0.99752182 0.99980478
[4345] 0.99660089 1.00514311 0.99815160 1.03307038 1.00009096 0.50082509
[4351] 1.02026753 1.00073627 1.00017135 0.96127211 1.00005698 1.00209541
[4357] 1.30436973 1.00005274 0.99995192 0.99994070 0.99987129 0.99942318
[4363] 1.00003075 0.73604676 1.00751015 1.00388225 1.00020001 0.99681970
[4369] 0.99664719 0.98421040 0.99603035 0.99805649 1.00191340 0.99936807
[4375] 1.00080729 0.99791438 0.98380406 1.00007227 1.02693336 1.04468495
[4381] 1.00000203 0.99987543 1.00241387 0.87517710 0.99299214 1.00076863
[4387] 0.99998624 1.03336327 0.99891288 1.03807335 0.95143429 1.00021127
[4393] 0.61600068 0.96493535 0.92424645 0.99994604 1.20623311 0.98610713
[4399] 0.99998960 1.01463118 1.01460800 0.87996383 1.00509548 1.00092313
[4405] 0.99985327 0.99954950 0.99038042 0.99999193 1.27985729 1.00175242
[4411] 1.00187111 0.99992231 0.99849471 0.99763684 0.98243566 1.02296172
[4417] 0.99997296 0.99517015 1.00009016 1.00019501 0.99868809 1.00253306
[4423] 1.00007900 1.00014719 1.03898832 0.99998967 0.88230936 1.00684326
[4429] 0.54848035 1.00646286 1.01954816 0.99500436 1.00083456 1.00181706
[4435] 0.98447281 0.99835658 1.00010233 1.00026354 0.97778966 1.00040792
[4441] 0.99991901 0.98614246 1.00016258 1.00035620 1.06535598 0.98592574
[4447] 1.00049869 0.99999368 1.00005988 0.99983378 0.99987946 0.99998297
[4453] 1.00293302 1.00135214 0.99678843 0.99962964 0.99665271 0.99897155
[4459] 1.01339468 0.99998157 0.99999219 0.90853559 0.99865212 1.00015502
[4465] 0.99989271 1.00001921 1.16321678 0.99792989 1.00030251 0.99850793
[4471] 1.00011662 0.98990946 0.99989963 1.00011914 0.96453656 1.13012099
[4477] 0.99984943 1.03415247 0.99803528 1.00012394 1.00830966 0.99999108
[4483] 0.99999037 1.00007923 1.00070234 0.99795545 0.99993461 0.99815212
[4489] 0.99911401 0.99187999 0.99995238 1.00002282 1.01415942 0.99776856
[4495] 0.96577155 1.00424008 1.00061064 0.99749190 1.00000233 0.99722738
[4501] 0.92437201 1.00008327 0.87231297 1.01403996 0.99981694 1.00316232
[4507] 0.95575807 1.00011175 1.09260376 0.91805307 1.00327151 0.96961636
[4513] 0.99659266 1.00040643 0.99923239 0.99336947 1.00028430 0.85350652
[4519] 0.99918646 0.92937785 0.98628916 0.94268571 0.99968628 1.00150559
[4525] 0.99685392 1.00006031 1.01837062 0.99996269 1.00004498 1.03994774
[4531] 0.99707526 1.00060676 0.98504345 0.99986874 0.99999690 1.00134976
[4537] 1.00170649 1.00005684 0.99994786 1.00006642 1.00004694 1.00084450
[4543] 0.99978219 0.99756568 1.00000098 0.99936912 1.01519719 1.00004114
[4549] 0.97829202 0.99988309 0.99819324 1.00036944 1.04059257 0.99666505
[4555] 0.99996992 1.00002662 0.99984577 1.00063451 1.00109408 1.00109443
[4561] 0.97604974 1.01401932 1.00007965 0.69664702 1.00008107 1.00006390
[4567] 0.99271867 0.99709752 0.99599356 1.00028987 1.00034056 1.00311253
[4573] 0.98849989 0.99953377 0.95549597 0.89169355 1.00005046 0.97854679
[4579] 0.99722820 1.00052662 0.99988193 1.01058668 0.99555399 0.99991207
[4585] 0.99947626 0.96649873 1.00006436 1.00998700 0.99994715 1.00176437
[4591] 1.12214655 0.99672388 0.99999496 0.99965400 0.99803917 0.96158331
[4597] 0.99999293 1.00017977 1.00248728 0.99994074 0.99659753 1.00004227
[4603] 1.22971662 1.27419520 0.99989493 0.99968539 0.99973598 1.28714028
[4609] 0.99985053 0.99989898 0.99983292 1.19354310 1.24345644 1.21787308
[4615] 0.99992268 0.97768915 1.26737174 0.83200310 0.99949907 1.14719006
[4621] 1.21140464 1.27293847 1.22066049 0.99937463 0.99984750 0.99989850
[4627] 0.99469544 0.99989679 0.99979744 0.99983276 0.99880911 0.99993733
[4633] 1.23142412 1.22832676 1.20300360 1.21757365 0.99999851 0.99536103
[4639] 1.22626129 0.99993736 1.19486084 0.99989385 1.27356454 0.96860655
[4645] 0.99989725 0.99990551 1.24667989 0.99988535 0.97289427 0.99999889
[4651] 1.14646241 1.27760748 1.27520242 1.28630561 1.18119525 0.99996752
[4657] 0.99957140 0.99987522 0.99979258 0.99989195 0.99998621 1.26841145
[4663] 0.99989015 1.26263447 0.99989905 1.32397834 1.24676873 1.20535308
[4669] 1.00000330 0.99992445 0.83326683 1.19458435 0.99989667 1.22068051
[4675] 1.21425119 0.99989897 0.99981261 0.83443157 0.99985743 1.25149034
[4681] 1.18533787 0.99986619 0.99986781 0.99989771 1.22965715 1.27951202
[4687] 1.25202092 1.20896381 0.95466174 0.99948372 1.17340144 0.99990013
[4693] 1.24673835 1.00006145 0.99984855 0.99991260 0.99989713 0.99989637
[4699] 0.99988694 1.34312471 0.99968689 0.99995270 1.42095331 0.99990197
[4705] 1.27288326 1.26220931 1.25953067 0.99990666 1.39030023 0.99990536
[4711] 1.35015148 1.38022520 1.01705912 1.26094172 0.99987335 0.99990542
[4717] 1.26649053 1.23876585 0.99989930 0.99996963 1.25073427 1.34878986
[4723] 1.22028891 1.38301562 0.99967735 1.20028323 1.28141379 1.23954222
[4729] 0.91819834 1.21788810 0.87843842 0.99668855 1.15234144 0.99990386
[4735] 0.99989884 0.99878727 0.96980207 0.99990278 0.99989881 0.99987188
[4741] 0.99989723 1.16015396 0.83571212 1.34854295 1.32848354 0.99987752
[4747] 1.21251786 1.29173935 0.99985622 1.21400528 0.99989133 1.33012697
[4753] 1.09777279 1.16225818 1.26347769 0.99946638Conclusion
From the plot above, we observed that the geographically weighted model performed slightly better than the general logistic regression model.