Take home assignment 1

Published

January 30, 2023

Intro

Water is an important resource to mankind. Clean and accessible water is critical to human health. It provides a healthy environment, a sustainable economy, reduces poverty and ensures peace and security. Yet over 40% of the global population does not have access to sufficient clean water. By 2025, 1.8 billion people will be living in countries or regions with absolute water scarcity, according to UN-Water. The lack of water poses a major threat to several sectors, including food security. Agriculture uses about 70% of the world’s accessible freshwater.

Developing countries are most affected by water shortages and poor water quality. Up to 80% of illnesses in the developing world are linked to inadequate water and sanitation. Despite technological advancement, providing clean water to the rural community is still a major development issues in many countries globally, especially countries in the Africa continent.

Objectives

Exploratory Spatial Data Analysis (ESDA)

  • Derive kernel density maps of functional and non-functional water points. Using appropriate tmap functions

  • Display the kernel density maps on openstreetmap of Osub State, Nigeria.

  • Describe the spatial patterns revealed by the kernel density maps. Highlight the advantage of kernel density map over point map.

Second-order Spatial Point Patterns Analysis

With reference to the spatial point patterns observed in ESDA:

  • Formulate the null hypothesis and alternative hypothesis and select the confidence level.

  • Perform the test by using appropriate Second order spatial point patterns analysis technique.

  • With reference to the analysis results, draw statistical conclusions.

Spatial Correlation Analysis

In this section, you are required to confirm statistically if the spatial distribution of functional and non-functional water points are independent from each other.

  • Formulate the null hypothesis and alternative hypothesis and select the confidence level.

  • Perform the test by using appropriate Second order spatial point patterns analysis technique.

  • With reference to the analysis results, draw statistical conclusions.

Importing packages

pacman::p_load(sf, tidyverse, tmap, maptools, raster, spatstat, sfdep)

Data wrangling

Import Aspatial data

First we take the Wpdx dataset and filter out to get only one country data: Nigeria, then filter out to get only one state: Osun

wp_nga <- read_csv("data/aspatial/WPdx.csv") %>%
  filter(`#clean_country_name` == "Nigeria", `#clean_adm1` == "Osun")

Import Geospatial data

geoNGA <- st_read(dsn = "data/geospatial", 
                  layer = "geoBoundaries-NGA-ADM2")%>%
  
  st_transform(crs = 26392)
Reading layer `geoBoundaries-NGA-ADM2' from data source 
  `C:\Study\Y3\S2\IS415\ELAbishek\IS415-GAA\Takehome_exercise\TakeHome1\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 774 features and 5 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2.668534 ymin: 4.273007 xmax: 14.67882 ymax: 13.89442
Geodetic CRS:  WGS 84

Now we take the geospatial dataset and we filter out to get only the data from Osun state

NGA <- st_read("data/geospatial",
               layer = "nga_admbnda_adm2")%>%
  filter(`ADM1_EN` == "Osun")%>%
  st_transform(crs = 26392)
Reading layer `nga_admbnda_adm2' from data source 
  `C:\Study\Y3\S2\IS415\ELAbishek\IS415-GAA\Takehome_exercise\TakeHome1\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 774 features and 16 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2.668534 ymin: 4.273007 xmax: 14.67882 ymax: 13.89442
Geodetic CRS:  WGS 84

Data pre processing

Convert Aspatial data into Geospatial

wp_nga$Geometry = st_as_sfc(wp_nga$`New Georeferenced Column`)
glimpse(wp_nga)
Rows: 5,557
Columns: 71
$ row_id                        <dbl> 429123, 70566, 70578, 66401, 422190, 422…
$ `#source`                     <chr> "GRID3", "Federal Ministry of Water Reso…
$ `#lat_deg`                    <dbl> 8.020000, 7.317741, 7.759448, 8.031187, …
$ `#lon_deg`                    <dbl> 5.060000, 4.785507, 4.563998, 4.637400, …
$ `#report_date`                <chr> "08/29/2018 12:00:00 AM", "05/11/2015 12…
$ `#status_id`                  <chr> "Unknown", "No", "No", "No", "Unknown", …
$ `#water_source_clean`         <chr> NA, "Protected Shallow Well", "Borehole"…
$ `#water_source_category`      <chr> NA, "Well", "Well", "Well", NA, NA, "Wel…
$ `#water_tech_clean`           <chr> "Tapstand", "Mechanized Pump", "Mechaniz…
$ `#water_tech_category`        <chr> "Tapstand", "Mechanized Pump", "Mechaniz…
$ `#facility_type`              <chr> "Improved", "Improved", "Improved", "Imp…
$ `#clean_country_name`         <chr> "Nigeria", "Nigeria", "Nigeria", "Nigeri…
$ `#clean_adm1`                 <chr> "Osun", "Osun", "Osun", "Osun", "Osun", …
$ `#clean_adm2`                 <chr> "Ifedayo", "Atakumosa East", "Osogbo", "…
$ `#clean_adm3`                 <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#clean_adm4`                 <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#install_year`               <dbl> NA, NA, NA, 2004, NA, NA, 2006, 2014, 20…
$ `#installer`                  <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#rehab_year`                 <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#rehabilitator`              <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#management_clean`           <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, "Com…
$ `#status_clean`               <chr> NA, "Abandoned/Decommissioned", "Abandon…
$ `#pay`                        <chr> NA, "No", "No", "No", NA, NA, "No", "No"…
$ `#fecal_coliform_presence`    <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#fecal_coliform_value`       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#subjective_quality`         <chr> NA, "Acceptable quality", "Acceptable qu…
$ `#activity_id`                <chr> "6054e946-2573-45bf-ab7c-0ddaa68a61b4", …
$ `#scheme_id`                  <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#wpdx_id`                    <chr> "6FW723C6+222", "6FV68Q9P+36R", "6FV6QH5…
$ `#notes`                      <chr> "Rt Hon Kola Oluwawole Water Tap", "Temi…
$ `#orig_lnk`                   <chr> "https://nigeria.africageoportal.com/dat…
$ `#photo_lnk`                  <chr> NA, "https://akvoflow-55.s3.amazonaws.co…
$ `#country_id`                 <chr> "NG", "NG", "NG", "NG", "NG", "NG", "NG"…
$ `#data_lnk`                   <chr> "https://catalog.waterpointdata.org/data…
$ `#distance_to_primary_road`   <dbl> 4474.22234, 10130.42742, 167.82235, 4133…
$ `#distance_to_secondary_road` <dbl> 1883.98780, 17466.35720, 838.91849, 1162…
$ `#distance_to_tertiary_road`  <dbl> 1885.874322, 2376.832183, 1181.107236, 9…
$ `#distance_to_city`           <dbl> 40100.268, 31549.222, 2449.293, 16704.19…
$ `#distance_to_town`           <dbl> 8120.871, 24652.907, 9463.295, 5176.899,…
$ water_point_history           <chr> "{\"2018-08-29\": {\"source\": \"GRID3\"…
$ rehab_priority                <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ water_point_population        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 0, 508, …
$ local_population_1km          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, 70, 647,…
$ crucialness_score             <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.78…
$ pressure_score                <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.69…
$ usage_capacity                <dbl> 250, 1000, 1000, 1000, 250, 250, 1000, 3…
$ is_urban                      <lgl> FALSE, FALSE, TRUE, FALSE, FALSE, FALSE,…
$ days_since_report             <dbl> 1483, 2689, 2689, 2700, 1483, 1483, 2688…
$ staleness_score               <dbl> 62.65911, 42.84384, 42.84384, 42.69554, …
$ latest_record                 <lgl> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE…
$ location_id                   <dbl> 358783, 239555, 239556, 230405, 358062, …
$ cluster_size                  <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ `#clean_country_id`           <chr> "NGA", "NGA", "NGA", "NGA", "NGA", "NGA"…
$ `#country_name`               <chr> "Nigeria", "Nigeria", "Nigeria", "Nigeri…
$ `#water_source`               <chr> "Tap", "Improved Protected dug well", "I…
$ `#water_tech`                 <chr> NA, "Motorised", "Motorised", "Motorised…
$ `#status`                     <chr> NA, "Non-functional Abandoned", "Non-fun…
$ `#adm2`                       <chr> NA, "Atakumosa East", "Osogbo", "Odo-Oti…
$ `#adm3`                       <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ `#management`                 <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, "Com…
$ `#adm1`                       <chr> NA, "Osun", "Osun", "Osun", NA, NA, "Osu…
$ `New Georeferenced Column`    <chr> "POINT (5.06 8.02)", "POINT (4.7855068 7…
$ lat_deg_original              <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ lat_lon_deg                   <chr> "(8.02°, 5.06°)", "(7.3177411°, 4.785506…
$ lon_deg_original              <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
$ public_data_source            <chr> "https://catalog.waterpointdata.org/data…
$ converted                     <chr> NA, "#status_id, #water_source, #pay, #s…
$ count                         <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ created_timestamp             <chr> "12/06/2021 09:12:57 PM", "06/30/2020 12…
$ updated_timestamp             <chr> "12/06/2021 09:12:57 PM", "06/30/2020 12…
$ Geometry                      <POINT> POINT (5.06 8.02), POINT (4.785507 7.3…
wp_sf <- st_sf(wp_nga, crs=4326)
wp_sf
Simple feature collection with 5557 features and 70 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 4.032004 ymin: 7.060309 xmax: 5.06 ymax: 8.061898
Geodetic CRS:  WGS 84
# A tibble: 5,557 × 71
   row_id `#source`      #lat_…¹ #lon_…² #repo…³ #stat…⁴ #wate…⁵ #wate…⁶ #wate…⁷
 *  <dbl> <chr>            <dbl>   <dbl> <chr>   <chr>   <chr>   <chr>   <chr>  
 1 429123 GRID3             8.02    5.06 08/29/… Unknown <NA>    <NA>    Tapsta…
 2  70566 Federal Minis…    7.32    4.79 05/11/… No      Protec… Well    Mechan…
 3  70578 Federal Minis…    7.76    4.56 05/11/… No      Boreho… Well    Mechan…
 4  66401 Federal Minis…    8.03    4.64 04/30/… No      Boreho… Well    Mechan…
 5 422190 GRID3             7.87    4.88 08/29/… Unknown <NA>    <NA>    Tapsta…
 6 422064 GRID3             7.7     4.89 08/29/… Unknown <NA>    <NA>    Tapsta…
 7  65607 Federal Minis…    7.89    4.71 05/12/… No      Boreho… Well    Mechan…
 8  68989 Federal Minis…    7.51    4.27 05/07/… No      Boreho… Well    <NA>   
 9  67708 Federal Minis…    7.48    4.35 04/29/… Yes     Boreho… Well    Mechan…
10  66419 Federal Minis…    7.63    4.50 05/08/… Yes     Boreho… Well    Hand P…
# … with 5,547 more rows, 62 more variables: `#water_tech_category` <chr>,
#   `#facility_type` <chr>, `#clean_country_name` <chr>, `#clean_adm1` <chr>,
#   `#clean_adm2` <chr>, `#clean_adm3` <chr>, `#clean_adm4` <chr>,
#   `#install_year` <dbl>, `#installer` <chr>, `#rehab_year` <lgl>,
#   `#rehabilitator` <lgl>, `#management_clean` <chr>, `#status_clean` <chr>,
#   `#pay` <chr>, `#fecal_coliform_presence` <chr>,
#   `#fecal_coliform_value` <dbl>, `#subjective_quality` <chr>, …

Projection transformation

We then transform the dataset into appropriate crs = 26392 so that we can perform our further analysis

wp_sf <- wp_sf %>%
  st_transform(crs = 26392)

Selecting necessary columns

There is no need for the other columns, so we are taking just the column we need, just to make things faster in the long run

NGA <- NGA %>%
 dplyr::select(c(3:4, 8:9)) #adm1 and adm2 cols

Cleaning duplicate data

NGA$ADM2_EN[duplicated(NGA$ADM2_EN)==TRUE]
character(0)
duplicated_LGA <- NGA$ADM2_EN[duplicated(NGA$ADM2_EN)==TRUE]

duplicated_indices <- which(NGA$ADM2_EN %in% duplicated_LGA)

for (ind in duplicated_indices) {
  NGA$ADM2_EN[ind] <- paste(NGA$ADM2_EN[ind], NGA$ADM1_EN[ind], sep=", ")
}

Now that we have assurance that the data does not have any duplicate data, we may proceed with data wrangling

Data wrangling

#Replacing records where the status column is empty with "unknown" to prevent errors in the future
wp_sf <- wp_sf %>%
  rename(status_clean = '#status_clean') %>%
  dplyr::select(status_clean) %>%
  mutate(status_clean = replace_na(
    status_clean, "unknown"
  ))
wp_sf_osun <- wp_sf %>%
  mutate(`func_status` = case_when(
    `status_clean` %in% c("Functional", 
                          "Functional but not in use",
                          "Functional but needs repair") ~ 
      "Functional",
    `status_clean` %in% c("Abandoned/Decommissioned",
                               "Non-Functional due to dry season",
                               "Non-Functional",
                               "Abandoned",
                               "Non functional due to dry season") ~ 
      "Non-Functional",
    `status_clean` == "Unknown" ~ "Unknown"))

Separating functional and non functional waterpoints

Separating out and obtaining functional and non functional waterpoints

wp_functional <- wp_sf_osun %>%
  filter(status_clean %in%
           c("Functional",
             "Functional but not in use",
             "Functional but needs repair"))
wp_nonfunctional <- wp_sf_osun %>%
  filter(status_clean %in%
           c("Abandoned/Decommissioned",
             "Abandoned",
             "Non-Functional due to dry season",
             "Non-Functional",
             "Non functional due to dry season"))
wp_unknown_sf <- wp_sf_osun %>% filter(`status_clean` %in% 
                                     c("unknown"))
NGA_wp_sf <- NGA %>%
  mutate(`total_wp` = lengths(
    st_intersects(NGA, wp_sf_osun)
  )) %>%
  mutate(`wp_functional` = lengths(
    st_intersects(NGA, wp_functional)
  )) %>%
  mutate(`wp_nonfunctional` = lengths(
    st_intersects(NGA, wp_nonfunctional)
  )) %>%
  mutate(`wp_unknown_sf` = lengths(
    st_intersects(NGA, wp_unknown_sf)
  ))
glimpse(NGA)
Rows: 30
Columns: 5
$ ADM2_EN    <chr> "Aiyedade", "Aiyedire", "Atakumosa East", "Atakumosa West",…
$ ADM2_PCODE <chr> "NG030001", "NG030002", "NG030003", "NG030004", "NG030005",…
$ ADM1_EN    <chr> "Osun", "Osun", "Osun", "Osun", "Osun", "Osun", "Osun", "Os…
$ ADM1_PCODE <chr> "NG030", "NG030", "NG030", "NG030", "NG030", "NG030", "NG03…
$ geometry   <MULTIPOLYGON [m]> MULTIPOLYGON (((213526.6 34..., MULTIPOLYGON (…

Kernel Density Estimation

NG <- as_Spatial(NGA)
wpf <- as_Spatial(wp_functional)
wpnf <- as_Spatial(wp_nonfunctional)

Converting to sp

NG_sp <- as(NG, "SpatialPolygons")
wpf_sp <- as(wpf,"SpatialPoints")
wpnf_sp <- as(wpnf, "SpatialPoints")

Creation of owin object

NG_owin <- as(NG_sp, "owin")

Converting sp to ppp object

wpf_ppp <- as(wpf_sp, "ppp")
wpnf_ppp <- as(wpnf_sp, "ppp")
plot(wpf_ppp)

plot(wpnf_ppp)

wpf_ppp = wpf_ppp[NG_owin]
wpnf_ppp = wpnf_ppp[NG_owin]
plot(wpf_ppp)

plot(wpnf_ppp)

Checking for duplicate values

any(duplicated(wpf_ppp)) 
[1] FALSE
any(duplicated(wpnf_ppp)) 
[1] FALSE

Since no duplicate values were detected, we can proceed with the plotting as per normal

NGAf_bw <- density(wpf_ppp,
                              sigma=bw.ppl,
                              edge=TRUE,
                            kernel="gaussian") 
NGAnf_bw <- density(wpnf_ppp,
                              sigma=bw.ppl,
                              edge=TRUE,
                            kernel="gaussian")

Scaling of the ppp so that we can get accurate mapping that is consistent

wpf_ppp.km <- rescale(wpf_ppp, 1000, "km")
wpnf_ppp.km <- rescale(wpnf_ppp, 1000, "km")
bw <- bw.ppl(wpf_ppp)
bw
   sigma 
919.2953 
bw <- bw.ppl(wpnf_ppp)
bw
   sigma 
973.7385 
NGAf.bw <- density(wpf_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="gaussian")
NGAnf.bw <- density(wpnf_ppp.km, sigma=bw.ppl, edge=TRUE, kernel="gaussian")

plot(NGAnf.bw)

plot(NGAf.bw)

Converting KDE into grid object

gridded_NGAf_bw <- as.SpatialGridDataFrame.im(NGAf.bw)
spplot(gridded_NGAf_bw)

gridded_NGAnf_bw <- as.SpatialGridDataFrame.im(NGAnf.bw)
spplot(gridded_NGAnf_bw)

Converting gridded output into raster

NGAf_bw_raster <- raster(gridded_NGAf_bw)

NGAnf_bw_raster <- raster(gridded_NGAnf_bw)
NGAf_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.8948485, 0.9616045  (x, y)
extent     : 176.5032, 291.0438, 331.4347, 454.5201  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : v 
values     : -4.99773e-16, 10.55944  (min, max)
NGAnf_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.8948485, 0.9616045  (x, y)
extent     : 176.5032, 291.0438, 331.4347, 454.5201  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : v 
values     : -2.52505e-16, 9.25861  (min, max)
projection(NGAf_bw_raster) <- CRS("+init=EPSG:26392 +units=km")
NGAf_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.8948485, 0.9616045  (x, y)
extent     : 176.5032, 291.0438, 331.4347, 454.5201  (xmin, xmax, ymin, ymax)
crs        : +init=EPSG:26392 +units=km 
source     : memory
names      : v 
values     : -4.99773e-16, 10.55944  (min, max)
projection(NGAnf_bw_raster) <- CRS("+init=EPSG:26392 +units=km")
NGAnf_bw_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.8948485, 0.9616045  (x, y)
extent     : 176.5032, 291.0438, 331.4347, 454.5201  (xmin, xmax, ymin, ymax)
crs        : +init=EPSG:26392 +units=km 
source     : memory
names      : v 
values     : -2.52505e-16, 9.25861  (min, max)

KDE on open street map

Plotting KDE for functional waterpoints

tmap_mode('view')+ #Functional KDE
  tm_shape(NGAf_bw_raster) + 
  tm_raster("v", palette = "YlOrBr") +
  tm_basemap("OpenStreetMap") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
kde_func <- tm_shape(NGAf_bw_raster) + 
  tm_raster("v", palette = "YlOrBr", title="") +
  tm_layout(
    legend.position = c("right", "bottom"), 
    main.title = "Functional",
    frame = FALSE
  )

kde_func +
  tm_shape(NGA) +
  tm_borders() +
  tm_text("ADM2_EN", size = 0.6)

Plotting KDE for non functional waterpoints

tmap_mode('view')+ #Non-functional KDE
  tm_shape(NGAnf_bw_raster) +
  tm_raster("v", alpha = 0.75, palette = "YlGnBu") +
  tm_basemap("OpenStreetMap") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
kde_nonfunc <- tm_shape(NGAnf_bw_raster) + 
  tm_raster("v", palette = "YlGnBu", title="") +
  tm_layout(
    legend.position = c("right", "bottom"), 
    main.title = "Non-Functional",
    frame = FALSE
  )

kde_nonfunc +
  tm_shape(NGA) +
  tm_borders() +
  tm_text("ADM2_EN", size = 0.6)

Analysis

From the KDE plots done above we can see that there is a huge disparity in terms of the concentration of functional to nonfunctional waterpoints in the different LGAs of Osun state. There is a higher number of water points in the Northern parts of the state, but in that, the North Western LGAs have a higher concentration of Functional waterpoints, such as Ife North, Ejigbo, and Iwo. While the North Easter LGAs have a higher concentration of non functional water points, such as in LGAs like Osogobo, Irepodun, Boripe. Ife Central also has a really high concentration of non functional waterpoints in its Southern section.

Second order spatial point analysis

In order to perform second order spatial point analysis, in this case we are creating owin objects of some LGAs within Osun for observation

  • H0: Functional and non functional waterpoints are randomly distributed

  • H1: Functional and non functional waterpoints are not randomly distributed

  • Confidence level : 99%

  • Significance level (alpha) : 0.05

  • Reject null hypothesis if p-value is < 0.05

#Functional water points
IfeCentralowin <- NGA[NGA$ADM2_EN == "Ife Central",] %>%
    as('Spatial') %>%
    as('SpatialPolygons') %>%
    as('owin')

Ejigboowin <- NGA[NGA$ADM2_EN == "Ejigbo",] %>%
    as('Spatial') %>%
    as('SpatialPolygons') %>%
    as('owin')

#non functional points
EdeNorthowin <- NGA[NGA$ADM2_EN == "Ede North",] %>%
    as('Spatial') %>%
    as('SpatialPolygons') %>%
    as('owin')

EdeSouthowin <- NGA[NGA$ADM2_EN == "Ede South",] %>%
    as('Spatial') %>%
    as('SpatialPolygons') %>%
    as('owin')

plot(IfeCentralowin)

plot(Ejigboowin)

plot(EdeNorthowin)

plot(EdeSouthowin)

IfeCentralowin_ppp <- wpf_ppp[IfeCentralowin]
Ejigboowin_ppp <- wpf_ppp[Ejigboowin]
EdeNorthowin_ppp <- wpnf_ppp[EdeNorthowin]
EdeSouthowin_ppp <- wpnf_ppp[EdeSouthowin]
plot(IfeCentralowin_ppp)

plot(Ejigboowin_ppp)

plot(EdeNorthowin_ppp)

plot(EdeSouthowin_ppp)

Now that we have the owin objects with the functional and non functional water points plotted in them, we can start off by plotting the G function

Plotting G function for functional waterpoints

IfecentralFuncG = Gest(IfeCentralowin_ppp, correction = "border")
plot(IfecentralFuncG)

Spatial randomness test

IfecentralFunc.csr <- envelope(IfeCentralowin_ppp, Gest, nsim=100)
Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.
plot(IfecentralFunc.csr)

EjigboFuncG = Gest(Ejigboowin_ppp, correction = "border")
plot(EjigboFuncG)

EjigboFunc.csr <- envelope(Ejigboowin_ppp, Gest, nsim=100)
Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.
plot(EjigboFunc.csr)

Analysis

In both of the spatial randomness tests for functional waterpoints in the regions of Ife Central, and Ejigbo, we can see that the G(r) is significantly above both G(theo) and the envelope, indicating the functional waterpoints are clustered.Hence we reject the null hypothesis that functional waterpoints are randomly distributed with a 99% confidence

Plotting G function for non-functional waterpoints

EdNorthNonFuncG = Gest(EdeNorthowin_ppp, correction = "border")
plot(EdNorthNonFuncG)

EdNorthNonFunc.csr <- envelope(EdeNorthowin_ppp, Gest, nsim=100)
Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.
plot(EdNorthNonFunc.csr)

EdSouthNonFuncG = Gest(EdeSouthowin_ppp, correction = "border")
plot(EdSouthNonFuncG)

EdSouthNonFunc.csr <- envelope(EdeSouthowin_ppp, Gest, nsim=100)
Generating 100 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99,  100.

Done.
plot(EdSouthNonFunc.csr)

In both of the spatial randomness tests for functional waterpoints in the regions of Ede North, and Ede South, we can see that the G(r) is significantly above both G(theo) and the envelope, indicating the non functional waterpoints are clustered.Hence we reject the null hypothesis that functional waterpoints are randomly distributed with a 99% confidence

Spatial correlation analysis

Local Colocation Quotients (LCLQ)

  • H0: The Functional Water Points in Osun are not co-located with the Non-Functional Water Points

  • H1: The Functional Water Points in Osun are co-located with the Non-Functional Water Points

  • Confidence level : 95%

  • Significance level (alpha) : 0.05

  • The null hypothesis will be rejected if p-value < 0.05.

wp_sf_osun_kp <- wp_sf_osun %>%
  filter(`func_status` %in% c("Functional", "Non-Functional"))
functional_points <- wp_sf_osun_kp %>%
  filter(`func_status` == "Functional") %>%
  dplyr::pull(`func_status`)

nonfunctional_points <- wp_sf_osun_kp %>%
  filter(`func_status` == "Non-Functional") %>%
  dplyr::pull(`func_status`)

Nearest neighbours

nb <- include_self(
  st_knn(st_geometry(wp_sf_osun_kp),6))

Weight matrix

wt <- st_kernel_weights(nb,
                        wp_sf_osun_kp,
                        "gaussian",
                        adaptive = TRUE)

CoLocation Quotient (LCLQ)

LCLQc <- local_colocation(functional_points,
                         nonfunctional_points,
                         nb,
                         wt,
                         39)
LCLQ_waterpoints <- cbind(wp_sf_osun_kp, LCLQc)
LCLQ_waterpoints <- LCLQ_waterpoints %>% 
  mutate(
    `p_sim_Non.Functional` = replace(`p_sim_Non.Functional`, `p_sim_Non.Functional` > 0.05, NA),
    `Non.Functional` = ifelse(`p_sim_Non.Functional` > 0.05, NA, `Non.Functional`))

LCLQ_waterpoints <- LCLQ_waterpoints %>% mutate(`size` = ifelse(is.na(`Non.Functional`), 1, 5))

Analysis

tmap_mode('view')
tm_view(set.zoom.limits=c(9, 15),
        bbox = st_bbox(filter(LCLQ_waterpoints, !is.na(`Non.Functional`)))) +
  tm_shape(NGA) +
  tm_borders() +
  tm_shape(LCLQ_waterpoints) +
  tm_dots(col="Non.Functional",
          palette=c("cyan", "grey"),
          size = "size",
          scale=0.15,
          border.col = "black",
          border.lwd = 0.5,
          alpha=0.5,
          title="LCLQ"
          )

Conclusion

In general the LCLQ value is just slightly less than 1 for statstically significant LCLQ (i.e: p value is < 0.05) . This shows that for a functional waterpoint it is less likely to have a non functional waterpoint in its neighbourhood. This proportion represents the waterpoints proportion across Osun very well.

tmap_mode('plot')