pacman::p_load(spdep, tmap, sf, blorr, caret, corrplot, ggpubr, NbClust, GWmodel, tidyverse, funModeling, skimr,report)In class Exercise5
Setting the scene
To build explanatory model to discover factor affecting water point statues in Osun State, Nigeria,
Study area: Orun State, Negeria
Data sets:
Osun.rds, contains LGAs boundaries of Osun State. It is in sf polygon data frame, and
Osun_wp_sf.rds, contained water points within Osun State. It is in sf point data frame.
Model Varibales
Dependent variable: Water points status(i.e. functional/non-functional)
Independent variables:
distance_to_primary_road.
distance_to_secondary _road
distance_to_tertiary_road.
distance_to_city
distance_to_town
water_point_population
local_population_1km
usage_capacity
is_urban
water_source_clean
Getting start
Create In-class Exercise 5 folder
Write a code chunk to load the following packages: sf, tidyverse, funModeling, blorr,corrplot, ggpubr,sf,spdep,GWmodel, tmap, skimr,caret
Data Import
In this in-class exercise, two data sets will be used. They are:
Osun <- read_rds("rds/Osun.rds")
Osun_wp_sf <- read_rds("rds/Osun_wp_sf.rds")Osun_wp_sf %>%
freq(input = 'status')Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
of ggplot2 3.3.4.
ℹ The deprecated feature was likely used in the funModeling package.
Please report the issue at <https://github.com/pablo14/funModeling/issues>.
status frequency percentage cumulative_perc
1 TRUE 2642 55.5 55.5
2 FALSE 2118 44.5 100.0tmap_mode("view")tmap mode set to interactive viewingtm_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))Exploratory Data Analysis
Summary Statics with skimr.
Osun_wp_sf %>%
skim()Warning: Couldn't find skimmers for class: sfc_POINT, sfc; No user-defined `sfl`
provided. Falling back to `character`.| 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 | ▁▁▇▁▁ |
Osun_wp_sf_clean <- Osun_wp_sf %>%
filter_at(vars(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
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 Analysis
Osun_wp <- Osun_wp_sf_clean %>%
select(c(7,35:39,42:43,46:47,57)) %>%
st_set_geometry(NULL)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")
Building a Logistic Regression Models
model <- glm(status ~ distance_to_primary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
data = Osun_wp_sf_clean,
family = binomial(link ='logit'))Instead of using typical R report,
blr_regress(model) Model Overview
------------------------------------------------------------------------
Data Set Resp Var Obs. Df. Model Df. Residual Convergence
------------------------------------------------------------------------
data status 4756 4755 4745 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 0.3731 0.1088 3.4303 6e-04
distance_to_primary_road 1 0.0000 0.0000 -0.7328 0.4637
distance_to_tertiary_road 1 1e-04 0.0000 4.7127 0.0000
distance_to_city 1 0.0000 0.0000 -4.7653 0.0000
distance_to_town 1 0.0000 0.0000 -5.4356 0.0000
is_urbanTRUE 1 -0.2843 0.0785 -3.6210 3e-04
usage_capacity1000 1 -0.6222 0.0697 -8.9270 0.0000
water_source_cleanProtected Shallow Well 1 0.4986 0.0851 5.8559 0.0000
water_source_cleanProtected Spring 1 1.2944 0.4387 2.9505 0.0032
water_point_population 1 -5e-04 0.0000 -11.4007 0.0000
local_population_1km 1 3e-04 0.0000 19.4015 0.0000
-----------------------------------------------------------------------------------------------
Association of Predicted Probabilities and Observed Responses
---------------------------------------------------------------
% Concordant 0.7345 Somers' D 0.4691
% Discordant 0.2655 Gamma 0.4691
% Tied 0.0000 Tau-a 0.2317
Pairs 5585188 c 0.7345
---------------------------------------------------------------report(model)We fitted a logistic model (estimated using ML) to predict status with
distance_to_primary_road (formula: status ~ distance_to_primary_road +
distance_to_tertiary_road + distance_to_city + distance_to_town + is_urban +
usage_capacity + water_source_clean + water_point_population +
local_population_1km). The model's explanatory power is moderate (Tjur's R2 =
0.16). The model's intercept, corresponding to distance_to_primary_road = 0, is
at 0.37 (95% CI [0.16, 0.59], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_tertiary_road (formula:
status ~ distance_to_primary_road + distance_to_tertiary_road +
distance_to_city + distance_to_town + is_urban + usage_capacity +
water_source_clean + water_point_population + local_population_1km). The
model's explanatory power is moderate (Tjur's R2 = 0.16). The model's
intercept, corresponding to distance_to_tertiary_road = 0, is at 0.37 (95% CI
[0.16, 0.59], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_city (formula: status ~
distance_to_primary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + is_urban + usage_capacity + water_source_clean +
water_point_population + local_population_1km). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
distance_to_city = 0, is at 0.37 (95% CI [0.16, 0.59], p < .001). Within this
model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with distance_to_town (formula: status ~
distance_to_primary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + is_urban + usage_capacity + water_source_clean +
water_point_population + local_population_1km). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
distance_to_town = 0, is at 0.37 (95% CI [0.16, 0.59], p < .001). Within this
model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with is_urban (formula: status ~
distance_to_primary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + is_urban + usage_capacity + water_source_clean +
water_point_population + local_population_1km). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
is_urban = [?], is at 0.37 (95% CI [0.16, 0.59], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with usage_capacity (formula: status ~
distance_to_primary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + is_urban + usage_capacity + water_source_clean +
water_point_population + local_population_1km). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
usage_capacity = 300, is at 0.37 (95% CI [0.16, 0.59], p < .001). Within this
model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with water_source_clean (formula: status
~ distance_to_primary_road + distance_to_tertiary_road + distance_to_city +
distance_to_town + is_urban + usage_capacity + water_source_clean +
water_point_population + local_population_1km). The model's explanatory power
is moderate (Tjur's R2 = 0.16). The model's intercept, corresponding to
water_source_clean = Borehole, is at 0.37 (95% CI [0.16, 0.59], p < .001).
Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation., We fitted a logistic model
(estimated using ML) to predict status with water_point_population (formula:
status ~ distance_to_primary_road + distance_to_tertiary_road +
distance_to_city + distance_to_town + is_urban + usage_capacity +
water_source_clean + water_point_population + local_population_1km). The
model's explanatory power is moderate (Tjur's R2 = 0.16). The model's
intercept, corresponding to water_point_population = 0, is at 0.37 (95% CI
[0.16, 0.59], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation. and We fitted a logistic
model (estimated using ML) to predict status with local_population_1km
(formula: status ~ distance_to_primary_road + distance_to_tertiary_road +
distance_to_city + distance_to_town + is_urban + usage_capacity +
water_source_clean + water_point_population + local_population_1km). The
model's explanatory power is moderate (Tjur's R2 = 0.16). The model's
intercept, corresponding to local_population_1km = 0, is at 0.37 (95% CI [0.16,
0.59], p < .001). Within this model:
- The effect of distance to primary road is statistically non-significant and
negative (beta = -4.75e-06, 95% CI [-1.75e-05, 7.95e-06], p = 0.464; Std. beta
= -0.03, 95% CI [-0.10, 0.04])
- The effect of distance to tertiary road is statistically significant and
positive (beta = 9.75e-05, 95% CI [5.71e-05, 1.38e-04], p < .001; Std. beta =
0.16, 95% CI [0.10, 0.23])
- The effect of distance to city is statistically significant and negative
(beta = -1.69e-05, 95% CI [-2.38e-05, -9.95e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.11])
- The effect of distance to town is statistically significant and negative
(beta = -1.54e-05, 95% CI [-2.09e-05, -9.83e-06], p < .001; Std. beta = -0.19,
95% CI [-0.26, -0.12])
- The effect of is urbanTRUE is statistically significant and negative (beta =
-0.28, 95% CI [-0.44, -0.13], p < .001; Std. beta = -0.28, 95% CI [-0.44,
-0.13])
- The effect of usage capacity [1000] is statistically significant and negative
(beta = -0.62, 95% CI [-0.76, -0.49], p < .001; Std. beta = -0.62, 95% CI
[-0.76, -0.49])
- The effect of water source clean [Protected Shallow Well] is statistically
significant and positive (beta = 0.50, 95% CI [0.33, 0.67], p < .001; Std. beta
= 0.50, 95% CI [0.33, 0.67])
- The effect of water source clean [Protected Spring] is statistically
significant and positive (beta = 1.29, 95% CI [0.49, 2.23], p = 0.003; Std.
beta = 1.29, 95% CI [0.49, 2.23])
- The effect of water point population is statistically significant and
negative (beta = -5.11e-04, 95% CI [-6.02e-04, -4.27e-04], p < .001; Std. beta
= -0.75, 95% CI [-0.88, -0.62])
- The effect of local population 1km is statistically significant and positive
(beta = 3.46e-04, 95% CI [3.12e-04, 3.82e-04], p < .001; Std. beta = 1.45, 95%
CI [1.31, 1.60])
Standardized parameters were obtained by fitting the model on a standardized
version of the dataset. 95% Confidence Intervals (CIs) and p-values were
computed using a Wald z-distribution approximation.blr_confusion_matrix(model, cutoff = 0.5)Confusion Matrix and Statistics
Reference
Prediction FALSE TRUE
0 1292 740
1 822 1902
Accuracy : 0.6716
No Information Rate : 0.4445
Kappa : 0.3324
McNemars's Test P-Value : 0.0404
Sensitivity : 0.7199
Specificity : 0.6112
Pos Pred Value : 0.6982
Neg Pred Value : 0.6358
Prevalence : 0.5555
Detection Rate : 0.3999
Detection Prevalence : 0.5728
Balanced Accuracy : 0.6655
Precision : 0.6982
Recall : 0.7199
'Positive' Class : 1Osun_wp_sp <- Osun_wp_sf_clean %>%
select(c(status,
distance_to_primary_road,
distance_to_secondary_road,
distance_to_tertiary_road,
distance_to_city,
distance_to_town,
water_point_population,
local_population_1km,
is_urban,
usage_capacity,
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 : 11
names : status, distance_to_primary_road, distance_to_secondary_road, distance_to_tertiary_road, distance_to_city, distance_to_town, water_point_population, local_population_1km, is_urban, usage_capacity, water_source_clean
min values : 0, 0.014461356813335, 0.152195902540837, 0.017815121653488, 53.0461399623541, 30.0019777713073, 0, 0, 0, 1000, Borehole
max values : 1, 26909.8616132094, 19559.4793799085, 10966.2705628969, 47934.343603562, 44020.6393368124, 29697, 36118, 1, 300, Protected Spring bw.fixed <- bw.ggwr(status ~ distance_to_primary_road +
distance_to_secondary_road +
distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
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 -2889
1 -2836
2 -2830
3 -2829
4 -2829
5 -2829
Fixed bandwidth: 95768.67 AICc value: 5684.357
Iteration Log-Likelihood:(With bandwidth: 59200.13 )
=========================
0 -2875
1 -2818
2 -2810
3 -2808
4 -2808
5 -2808
Fixed bandwidth: 59200.13 AICc value: 5646.785
Iteration Log-Likelihood:(With bandwidth: 36599.53 )
=========================
0 -2847
1 -2781
2 -2768
3 -2765
4 -2765
5 -2765
6 -2765
Fixed bandwidth: 36599.53 AICc value: 5575.148
Iteration Log-Likelihood:(With bandwidth: 22631.59 )
=========================
0 -2798
1 -2719
2 -2698
3 -2693
4 -2693
5 -2693
6 -2693
Fixed bandwidth: 22631.59 AICc value: 5466.883
Iteration Log-Likelihood:(With bandwidth: 13998.93 )
=========================
0 -2720
1 -2622
2 -2590
3 -2581
4 -2580
5 -2580
6 -2580
7 -2580
Fixed bandwidth: 13998.93 AICc value: 5324.578
Iteration Log-Likelihood:(With bandwidth: 8663.649 )
=========================
0 -2601
1 -2476
2 -2431
3 -2419
4 -2417
5 -2417
6 -2417
7 -2417
Fixed bandwidth: 8663.649 AICc value: 5163.61
Iteration Log-Likelihood:(With bandwidth: 5366.266 )
=========================
0 -2436
1 -2268
2 -2194
3 -2167
4 -2161
5 -2161
6 -2161
7 -2161
8 -2161
9 -2161
Fixed bandwidth: 5366.266 AICc value: 4990.587
Iteration Log-Likelihood:(With bandwidth: 3328.371 )
=========================
0 -2157
1 -1922
2 -1802
3 -1739
4 -1713
5 -1713
Fixed bandwidth: 3328.371 AICc value: 4798.288
Iteration Log-Likelihood:(With bandwidth: 2068.882 )
=========================
0 -1751
1 -1421
2 -1238
3 -1133
4 -1084
5 -1084
Fixed bandwidth: 2068.882 AICc value: 4837.017
Iteration Log-Likelihood:(With bandwidth: 4106.777 )
=========================
0 -2297
1 -2095
2 -1997
3 -1951
4 -1938
5 -1936
6 -1936
7 -1936
8 -1936
Fixed bandwidth: 4106.777 AICc value: 4873.161
Iteration Log-Likelihood:(With bandwidth: 2847.289 )
=========================
0 -2036
1 -1771
2 -1633
3 -1558
4 -1525
5 -1525
Fixed bandwidth: 2847.289 AICc value: 4768.192
Iteration Log-Likelihood:(With bandwidth: 2549.964 )
=========================
0 -1941
1 -1655
2 -1503
3 -1417
4 -1378
5 -1378
Fixed bandwidth: 2549.964 AICc value: 4762.212
Iteration Log-Likelihood:(With bandwidth: 2366.207 )
=========================
0 -1874
1 -1573
2 -1410
3 -1316
4 -1274
5 -1274
Fixed bandwidth: 2366.207 AICc value: 4773.081
Iteration Log-Likelihood:(With bandwidth: 2663.532 )
=========================
0 -1979
1 -1702
2 -1555
3 -1474
4 -1438
5 -1438
Fixed bandwidth: 2663.532 AICc value: 4762.568
Iteration Log-Likelihood:(With bandwidth: 2479.775 )
=========================
0 -1917
1 -1625
2 -1468
3 -1380
4 -1339
5 -1339
Fixed bandwidth: 2479.775 AICc value: 4764.294
Iteration Log-Likelihood:(With bandwidth: 2593.343 )
=========================
0 -1956
1 -1674
2 -1523
3 -1439
4 -1401
5 -1401
Fixed bandwidth: 2593.343 AICc value: 4761.813
Iteration Log-Likelihood:(With bandwidth: 2620.153 )
=========================
0 -1965
1 -1685
2 -1536
3 -1453
4 -1415
5 -1415
Fixed bandwidth: 2620.153 AICc value: 4761.89
Iteration Log-Likelihood:(With bandwidth: 2576.774 )
=========================
0 -1950
1 -1667
2 -1515
3 -1431
4 -1393
5 -1393
Fixed bandwidth: 2576.774 AICc value: 4761.889
Iteration Log-Likelihood:(With bandwidth: 2603.584 )
=========================
0 -1960
1 -1678
2 -1528
3 -1445
4 -1407
5 -1407
Fixed bandwidth: 2603.584 AICc value: 4761.813
Iteration Log-Likelihood:(With bandwidth: 2609.913 )
=========================
0 -1962
1 -1680
2 -1531
3 -1448
4 -1410
5 -1410
Fixed bandwidth: 2609.913 AICc value: 4761.831
Iteration Log-Likelihood:(With bandwidth: 2599.672 )
=========================
0 -1958
1 -1676
2 -1526
3 -1443
4 -1405
5 -1405
Fixed bandwidth: 2599.672 AICc value: 4761.809
Iteration Log-Likelihood:(With bandwidth: 2597.255 )
=========================
0 -1957
1 -1675
2 -1525
3 -1441
4 -1403
5 -1403
Fixed bandwidth: 2597.255 AICc value: 4761.809 bw.fixed[1] 2599.672gwlr.fixed <- ggwr.basic(status ~
distance_to_primary_road+
distance_to_secondary_road+
distance_to_tertiary_road+
distance_to_town+
distance_to_city+
water_point_population+
local_population_1km+
is_urban+
usage_capacity+
water_source_clean,
data= Osun_wp_sp,
bw= bw.fixed,
family = "binomial",
kernel = "gaussian",
adaptive = FALSE,
longlat=FALSE) Iteration Log-Likelihood
=========================
0 -1958
1 -1676
2 -1526
3 -1443
4 -1405
5 -1405 gwr.fixed <- as.data.frame(gwlr.fixed$SDF)gwr.fixed <- gwr.fixed %>%
mutate(most = ifelse(
gwr.fixed$yhat >= 0.5, T,F))gwr.fixed$y <- as.factor(gwr.fixed$y)
gwr.fixed$most <- as.factor(gwr.fixed$most)
CM <- confusionMatrix(data=gwr.fixed$most, reference = gwr.fixed$y)
CMConfusion Matrix and Statistics
Reference
Prediction FALSE TRUE
FALSE 1824 263
TRUE 290 2379
Accuracy : 0.8837
95% CI : (0.8743, 0.8927)
No Information Rate : 0.5555
P-Value [Acc > NIR] : <2e-16
Kappa : 0.7642
Mcnemar's Test P-Value : 0.2689
Sensitivity : 0.8628
Specificity : 0.9005
Pos Pred Value : 0.8740
Neg Pred Value : 0.8913
Prevalence : 0.4445
Detection Rate : 0.3835
Detection Prevalence : 0.4388
Balanced Accuracy : 0.8816
'Positive' Class : FALSE
Osun_wp_sf_selected <- Osun_wp_sf_clean %>%
select(c(ADM2_EN, ADM2_PCODE,
ADM1_EN, ADM1_PCODE,
status))gwr_sf.fixed <- cbind(Osun_wp_sf_selected, gwr.fixed)tmap_mode("view")tmap mode set to interactive viewingprob_T <- tm_shape(Osun) +
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed) +
tm_dots(col = "yhat",
border.col = "gray60",
border.lwd =1)+
tm_view(set.zoom.limits = c(8,14))
prob_TRemoving the Variables and Building Logistic Regression Model
model2 <- glm(status ~ distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
data = Osun_wp_sf_clean,
family = binomial(link = 'logit'))
blr_regress(model2) 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_tertiary_road 1 1e-04 0.0000 4.9096 0.0000
distance_to_city 1 0.0000 0.0000 -5.2022 0.0000
distance_to_town 1 0.0000 0.0000 -5.4660 0.0000
is_urbanTRUE 1 -0.2667 0.0747 -3.5690 4e-04
usage_capacity1000 1 -0.6206 0.0697 -8.9081 0.0000
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
water_point_population 1 -5e-04 0.0000 -11.3902 0.0000
local_population_1km 1 3e-04 0.0000 19.4069 0.0000
-----------------------------------------------------------------------------------------------
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
---------------------------------------------------------------blr_confusion_matrix(model2, 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 : 1bw.fixed2 <- bw.ggwr(status ~ distance_to_tertiary_road +
distance_to_city +
distance_to_town +
is_urban +
usage_capacity +
water_source_clean +
water_point_population +
local_population_1km,
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: 5809.719
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 gwlr.fixed2 <- ggwr.basic(status ~distance_to_tertiary_road +
distance_to_city +
distance_to_town +
water_point_population +
local_population_1km +
is_urban +
usage_capacity +
water_source_clean,
data=Osun_wp_sp,
bw = bw.fixed2,
family = "binomial",
kernel = "gaussian",
adaptive = FALSE,
longlat = FALSE) Iteration Log-Likelihood
=========================
0 -1959
1 -1680
2 -1531
3 -1447
4 -1413
5 -1413 gwlr.fixed2 ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2022-12-18 02:52:45
Call:
ggwr.basic(formula = status ~ distance_to_tertiary_road + distance_to_city +
distance_to_town + water_point_population + local_population_1km +
is_urban + usage_capacity + water_source_clean, data = Osun_wp_sp,
bw = bw.fixed2, family = "binomial", kernel = "gaussian",
adaptive = FALSE, longlat = FALSE)
Dependent (y) variable: status
Independent variables: distance_to_tertiary_road distance_to_city distance_to_town water_point_population local_population_1km is_urban usage_capacity 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_tertiary_road 1.001e-04 2.040e-05 4.910 9.13e-07
distance_to_city -1.764e-05 3.391e-06 -5.202 1.97e-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
is_urbanTRUE -2.667e-01 7.474e-02 -3.569 0.000358
usage_capacity1000 -6.206e-01 6.966e-02 -8.908 < 2e-16
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_tertiary_road ***
distance_to_city ***
distance_to_town ***
water_point_population ***
local_population_1km ***
is_urbanTRUE ***
usage_capacity1000 ***
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_tertiary_road -3.1622e-02 -4.5462e-04 9.1291e-05
distance_to_city -5.4555e-02 -6.5623e-04 -1.3507e-04
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
is_urbanTRUE -7.3554e+02 -3.4675e+00 -1.6596e+00
usage_capacity1000 -5.5889e+01 -1.0347e+00 -4.1960e-01
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_tertiary_road 6.3011e-04 0.0237
distance_to_city 1.5921e-04 0.0162
distance_to_town 2.4490e-04 0.0179
water_point_population 4.5879e-04 0.0765
local_population_1km 1.8479e-03 0.0333
is_urbanTRUE 1.0554e+00 995.1840
usage_capacity1000 3.9113e-01 9.2449
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: 2022-12-18 02:53:12 gwr.fixed2 <- as.data.frame(gwlr.fixed2$SDF)gwr.fixed2 <- gwr.fixed2 %>%
mutate(most = ifelse(
gwr.fixed2$yhat >= 0.5, T, F))gwr.fixed2$y <- as.factor(gwr.fixed2$y)
gwr.fixed2$most <- as.factor(gwr.fixed2$most)
CM2 <- confusionMatrix(data=gwr.fixed2$most, reference = gwr.fixed2$y, positive = "TRUE")
CM2Confusion 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 : 0.8986
Specificity : 0.8671
Pos Pred Value : 0.8942
Neg Pred Value : 0.8724
Prevalence : 0.5555
Detection Rate : 0.4992
Detection Prevalence : 0.5582
Balanced Accuracy : 0.8828
'Positive' Class : TRUE
gwr_sf.fixed2 <- cbind(Osun_wp_sf_selected, gwr.fixed2)tmap_mode("view")tmap mode set to interactive viewingprob_T2 <- tm_shape(Osun) +
tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf.fixed2) +
tm_dots(col = "yhat",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(8,14))
prob_T2Conclusion
After Removing the two variables, there is no improvement in True Positive, and the True Negative improved a little. Therefore, using gwLR model can be used when focusing on the non-functional water point ratio.