Take_homeexercise_two

Introduction

Rpub link: -=https://rpubs.com/sakiyasuda/675431

On September 22nd, 2020, the government of Mexico reported the number of COVID-10 cases in its territory surpassed 700,000. Nearly 2,000 cases of COVID-19 have been reported, on a daily basis, while the recorded number of death in the country is now more than 300,000. As can be seen from the above-mentioned statistics, Mexico is currently suffering severe damage and casualties, due to an ongoing worldwide pandemic.

In this case, I will be looking to analyze the Spatio-Temporal patterns of COVID-19 in the country, with focus on Central Mexico. To be more specific, this analysis will be on Mexico City - (9), Mexico State - (15), and Morelos State - (17).

Install and import libraries

The first step will be installation of necessary libraries that are necessary for data analysis from R packages.

packages = c('rgdal', 'sf', 'spdep', 'tmap', 'tidyverse', 'rgeos','prettydoc','plotly')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
  }
  library(p,character.only = T)
}

Getting the data into R enviroment

As mentioned, this analysis is looking to focus on a current pandemic situation in Mexico. I extracted the data from Mexico’s Secretary of Health, under Mexican government.

(http://datosabiertos.salud.gob.mx/gobmx/salud/datos_abiertos/).

mexico <- readOGR(dsn = "data/geospatial", layer="municipalities_COVID")

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\sunho\Documents\SMU\3.2\gis\Take home2\Take_home_Two\data\geospatial", layer: "municipalities_COVID"
## with 2465 features
## It has 198 fields

Data Wrangling

Filter the dataset into different regions

I divided and categorized the data by three regions, in 09, 15, and 17. Each number represents a different region: (9) for Mexico City, (15) for Mexico State, and (17) for Morelos State. For an overall analysis on Central Mexico, I combined these datasets. This way, not only will it enable a comparison between regions, but it will also allow an overall view on the degree of influence of the COVID-19 on Central Mexico.

mexico_09 <- mexico[(mexico$CVE_ENT == '09'),]
mexico_15 <- mexico[(mexico$CVE_ENT == '15'),]
mexico_17 <- mexico[(mexico$CVE_ENT == '17'),]

central_mexico <- mexico[(mexico$CVE_ENT == '09' | mexico$CVE_ENT == '15' | mexico$CVE_ENT == '17'),]

Visualising Regional Devlopment Indicator

Plot the area 09,15,16 and central mexico areas to check if the layers are well plotted.

plot(mexico_09, main = "Area 09")

plot(mexico_15, main = "Area 15")

plot(mexico_17, main = "ARea 17")

plot(central_mexico, main = "Central Mexico")

Clean data based on cumulative cases

I will be mainly focused on cumulative cases as it allows me to determine the number of observation that lies with the past value in the dataset. By using cumulative cases, I will be able to analyze the cases of each area in central Mexico.

I have filtered the dataset into Mexico new cases and cumulative cases.

mexico_09_new <- mexico_09[,c(1:6,19:38)]
mexico_15_new <- mexico_15[,c(1:6,19:38)]
mexico_17_new <- mexico_17[,c(1:6,19:38)]
central_mexico_new <- central_mexico[,c(1:6,51:70)]

mexico_09_cumu <- mexico_09[,c(1:6,51:70)]
mexico_15_cumu <- mexico_15[,c(1:6,51:70)]
mexico_17_cumu <- mexico_17[,c(1:6,51:70)]
central_mexico_cumu <- central_mexico[,c(1:6,51:70)]

In order to calculate the covid 19 rate per population I need to calculate the total sum of cumulative cases

mexico_09_cumu@data$`total_count` <-  as.numeric(apply(mexico_09_new@data[,7:26], 1, sum))
mexico_15_cumu@data$`total_count` <-  as.numeric(apply(mexico_15_new@data[,7:26], 1, sum))
mexico_17_cumu@data$`total_count` <-  as.numeric(apply(mexico_17_new@data[,7:26], 1, sum))
central_mexico_cumu@data$`total_count` <-  as.numeric(apply(central_mexico_new@data[,7:26], 1, sum))

Calculate the Covid-19 Rate per 10000 population I have summed up the new cases and divided into the total population to calculate the covid-rate for each state in central Mexico and overall central Mexico.

mexico_09_cumu@data$`covid_rate` <- (mexico_09_cumu@data$`total_count`*10000)/mexico_09_cumu@data$`Pop2020`
mexico_15_cumu@data$`covid_rate` <- (mexico_15_cumu@data$`total_count`*10000)/mexico_15_cumu@data$`Pop2020`
mexico_17_cumu@data$`covid_rate` <- (mexico_17_cumu@data$`total_count`*10000)/mexico_17_cumu@data$`Pop2020`
central_mexico_cumu@data$`covid_rate` <- (central_mexico_cumu@data$`total_count`*10000)/central_mexico_cumu@data$`Pop2020`

mexico_cum_09_sf <- st_as_sf(mexico_09_cumu) %>%
  select("CVE_ENT", "NOMGEO", "covid_rate")

mexico_cum_15_sf <- st_as_sf(mexico_15_cumu) %>%
  select("CVE_ENT", "NOMGEO", "covid_rate")

mexico_cum_17_sf <- st_as_sf(mexico_17_cumu) %>%
  select("CVE_ENT", "NOMGEO", "covid_rate")

central_mexico_sf <- st_as_sf(central_mexico_cumu) %>%
  select("CVE_ENT", "NOMGEO", "covid_rate")

central_mexico_sf <- st_as_sf(central_mexico_cumu)

Exploratiory Data Analysis

Let’s understand the cumulative cases in central Mexico. There were few cases for week 13 to week 16 but after that, it started to increase in cases till week 31. we can understand that the cases are gradually increasing and it slows down from week 31 to week 32.

let’s understand the covid19 rate using bar charts. From Mexico City 09, I can identity that Milpa Alta has the highest rate followed by Xochimilco

mexico_city_09_bar <- barplot(mexico_cum_09_sf$covid_rate, ylim = c(0, 200), main = "COVID 19 Rate in Mexico City 09", ylab="Covid 19 Rate") 
axis(1, at=mexico_city_09_bar, labels=mexico_cum_09_sf$NOMGEO, las=3, cex.lab=4, cex.axis=0.5)

From Mexico City 15, it’s very clear that Apaxco city has the highest rate

mexico_city_15_bar <- barplot(mexico_cum_15_sf$covid_rate, ylim = c(0, 200), main = "COVID 19 Rate in Mexico City 15", ylab="Covid 19 Rate") 
axis(1, at=mexico_city_15_bar, labels=mexico_cum_15_sf$NOMGEO, las=3, cex.lab=4, cex.axis=0.5)

From Mexico City 17, highest rate is Zacatepec follow by Tiayacapan and Puente de lxtla

mexico_city_17_bar <- barplot(mexico_cum_17_sf$covid_rate, ylim = c(0, 60), main = "COVID 19 Rate in Mexico City 17", ylab="Covid 19 Rate") 
axis(1, at=mexico_city_17_bar, labels=mexico_cum_17_sf$NOMGEO, las=3, cex.lab=4, cex.axis=0.5)

central_mexico_bar <- barplot(central_mexico_sf$covid_rate, ylim = c(0, 1500), main = "COVID 19 Rate in central_mexico", ylab="Covid 19 Rate") 
axis(1, at=central_mexico_bar, labels=central_mexico_sf$NOMGEO, las=3, cex.lab=4, cex.axis=0.5)

Spatial Analysis

Choloropleth Map

From the Choloropleth map, I can analyze that Area 09 have darker colours compared to other cities. Also, it spread to other regions by weeks

central_mexico_13 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul13, `geometry`) 

central_mexico_13_tmap <- tm_shape(central_mexico_13) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 13", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_14 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul14, `geometry`) 

central_mexico_14_tmap <- tm_shape(central_mexico_14) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 14", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
        


tmap_arrange(central_mexico_13_tmap,central_mexico_14_tmap, asp=1, ncol=2)

central_mexico_15 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul15, `geometry`) 

central_mexico_15_tmap <- tm_shape(central_mexico_15) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 15", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_16 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul16, `geometry`) 

central_mexico_16_tmap <- tm_shape(central_mexico_16) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 16", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_17 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul17, `geometry`) 

central_mexico_17_tmap <- tm_shape(central_mexico_17) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 17", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          


tmap_arrange(central_mexico_15_tmap,central_mexico_16_tmap,central_mexico_17_tmap, asp=1, ncol=3)

central_mexico_18 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul18, `geometry`) 

central_mexico_18_tmap <- tm_shape(central_mexico_18) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 18", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_19 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul19, `geometry`) 

central_mexico_19_tmap <- tm_shape(central_mexico_19) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 19", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_20 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul20, `geometry`) 

central_mexico_20_tmap <- tm_shape(central_mexico_20) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 20", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          


tmap_arrange(central_mexico_18_tmap,central_mexico_19_tmap,central_mexico_20_tmap, asp=1, ncol=3)

central_mexico_21 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul21, `geometry`) 

central_mexico_21_tmap <- tm_shape(central_mexico_21) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 21", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_22 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul22, `geometry`) 

central_mexico_22_tmap <- tm_shape(central_mexico_22) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 22", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_23 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul23, `geometry`) 

central_mexico_23_tmap <- tm_shape(central_mexico_23) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 23", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          


tmap_arrange(central_mexico_21_tmap,central_mexico_22_tmap,central_mexico_23_tmap, asp=1, ncol=3)

central_mexico_24 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul24, `geometry`) 

central_mexico_24_tmap <- tm_shape(central_mexico_24) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 24", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_25 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul25, `geometry`) 

central_mexico_25_tmap <- tm_shape(central_mexico_25) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 25", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_26 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul26, `geometry`) 

central_mexico_26_tmap <- tm_shape(central_mexico_26) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 26", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          


tmap_arrange(central_mexico_24_tmap,central_mexico_25_tmap,central_mexico_26_tmap, asp=1, ncol=3)

central_mexico_27 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul27, `geometry`) 

central_mexico_27_tmap <- tm_shape(central_mexico_27) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 27", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_28 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul28, `geometry`) 

central_mexico_28_tmap <- tm_shape(central_mexico_28) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 28", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_29 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul29, `geometry`) 

central_mexico_29_tmap <- tm_shape(central_mexico_26) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 29", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          

tmap_arrange(central_mexico_27_tmap,central_mexico_28_tmap,central_mexico_29_tmap, asp=1, ncol=3)

central_mexico_30 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul30, `geometry`) 

central_mexico_30_tmap <- tm_shape(central_mexico_27) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) +
          tm_layout(main.title = "week 30", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
central_mexico_31 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul31, `geometry`) 

central_mexico_31_tmap <- tm_shape(central_mexico_28) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 31", title.size = 0.5,main.title.position="center", legend.outside = TRUE)
          
          
central_mexico_32 <- central_mexico_sf %>%
  filter(CVE_ENT %in% c("09","15","17")) %>% 
  dplyr::select(`CVEGEO`, `CVE_ENT`, `CVE_MUN`, `NOMGEO`, `Pop2010`, `Pop2020`,`CUMULATIVE` = cumul32, `geometry`) 

central_mexico_32_tmap <- tm_shape(central_mexico_26) +
  tm_fill(col= "CUMULATIVE",
          title = "cumulative rate") +
          tm_borders(alpha = 0.5) + 
          tm_layout(main.title = "week 32", title.size = 0.5,main.title.position="center", legend.outside = TRUE)          

tmap_arrange(central_mexico_30_tmap,central_mexico_31_tmap,central_mexico_32_tmap, asp=1, ncol=3)

Let’s take a look at different 09,15 and 17 of the overall covid_rate. From the chart, it’s clear that most of the cases are from Mexico 09 and 17.

mexico_09_tmap <- qtm(mexico_09_cumu, "covid_rate", title = "Mexico_09")
mexico_15_tmap <- qtm(mexico_15_cumu, "covid_rate", title = "Mexico_15")
mexico_17_tmap <- qtm(mexico_17_cumu, "covid_rate", title = "Mexico_17")


tmap_arrange(mexico_09_tmap, mexico_15_tmap, mexico_17_tmap,asp=1, ncol=3)

qtm(central_mexico_cumu, "covid_rate", title = "central_mexico")

Spatial Neighbours using QUEEN and ROOK contintuity

I would compute the queen and rook contintuity map

QUEEN

central_mexico_cumu_wm_q <- poly2nb(central_mexico_cumu, queen=TRUE)

ROOK

central_mexico_cumu_wm_r <- poly2nb(central_mexico_cumu, queen=FALSE)

Visualise Queen contiguity

plot(central_mexico_cumu, border="lightgrey")
plot(central_mexico_cumu_wm_q, coordinates(central_mexico_cumu), pch = 19, cex = 0.6, add = TRUE, col = "red")

Visualise ROOK contiguity

plot(central_mexico_cumu, border="lightgrey")
plot(central_mexico_cumu_wm_r, coordinates(central_mexico_cumu), pch = 19, cex = 0.6, add = TRUE, col = "red")

Looking at the Queen and Rook Contiguity, I can identify 14 different links. Especially at the south-west od the map. Queen has more travel edges and corners. Hence, Queen continuity is more efficient for analysis.

Forming Weight Matrixes using Distance-based Neighbours

I will be analysing suitable weight matric for the analysis. From the output, I can identify that the distance is EPSG meter.

st_crs(central_mexico_sf)

## Coordinate Reference System:
##   User input: MEXICO_ITRF_2008_LCC 
##   wkt:
## PROJCRS["MEXICO_ITRF_2008_LCC",
##     BASEGEOGCRS["ITRF2008",
##         DATUM["International Terrestrial Reference Frame 2008",
##             ELLIPSOID["GRS 1980",6378137,298.257222101,
##                 LENGTHUNIT["metre",1]],
##             ID["EPSG",1061]],
##         PRIMEM["Greenwich",0,
##             ANGLEUNIT["Degree",0.0174532925199433]]],
##     CONVERSION["unnamed",
##         METHOD["Lambert Conic Conformal (2SP)",
##             ID["EPSG",9802]],
##         PARAMETER["Latitude of false origin",12,
##             ANGLEUNIT["Degree",0.0174532925199433],
##             ID["EPSG",8821]],
##         PARAMETER["Longitude of false origin",-102,
##             ANGLEUNIT["Degree",0.0174532925199433],
##             ID["EPSG",8822]],
##         PARAMETER["Latitude of 1st standard parallel",17.5,
##             ANGLEUNIT["Degree",0.0174532925199433],
##             ID["EPSG",8823]],
##         PARAMETER["Latitude of 2nd standard parallel",29.5,
##             ANGLEUNIT["Degree",0.0174532925199433],
##             ID["EPSG",8824]],
##         PARAMETER["Easting at false origin",2500000,
##             LENGTHUNIT["metre",1],
##             ID["EPSG",8826]],
##         PARAMETER["Northing at false origin",0,
##             LENGTHUNIT["metre",1],
##             ID["EPSG",8827]]],
##     CS[Cartesian,2],
##         AXIS["(E)",east,
##             ORDER[1],
##             LENGTHUNIT["metre",1,
##                 ID["EPSG",9001]]],
##         AXIS["(N)",north,
##             ORDER[2],
##             LENGTHUNIT["metre",1,
##                 ID["EPSG",9001]]]]

Fixed Distance Weight Matrix

centroids <- sf::st_centroid(central_mexico_sf$geometry)

coords <- st_coordinates(centroids)

knb <- knn2nb(knearneigh(coords,k=5, longlat = FALSE))
knn_lw <- nb2listw(knb, style = 'B')

k1dists <- unlist(nbdists(knb, coords, longlat = FALSE))
summary(k1dists)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1789    8508   11669   12690   15985   50477

Plot 1st Nearest Neighbours and Fixed Distance Link

Some of the areas in the fixed-distance link are not well connected compare to 1st nearest neighbours

wm_dmax <- dnearneigh(coords, 0, 20857, longlat = FALSE)
par(mfrow=c(1,2))

plot(central_mexico_sf$geometry, border="lightgrey", main="1st Nearest Neighbours")
plot(knb, coords, add=TRUE, col="red", length=0.08)
plot(central_mexico_sf$geometry, border="lightgrey", main="Fixed Distance Link")
plot(wm_dmax, coords, add=TRUE, pch = 19, cex = 0.6)

row-standardised weight matrix

Create the row-standardized weight matrix with nb2listw

rswm_q <- nb2listw(central_mexico_cumu_wm_q, zero.policy = TRUE)
summary(rswm_q)

## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 176 
## Number of nonzero links: 962 
## Percentage nonzero weights: 3.10563 
## Average number of links: 5.465909 
## Link number distribution:
## 
##  1  2  3  4  5  6  7  8  9 10 11 14 
##  3  3 18 41 31 31 22 13  9  3  1  1 
## 3 least connected regions:
## 721 739 765 with 1 link
## 1 most connected region:
## 761 with 14 links
## 
## Weights style: W 
## Weights constants summary:
##     n    nn  S0       S1      S2
## W 176 30976 176 71.10695 731.679

Moran’s I test

Perform Moran’s I statistic test using moran.test()

moran.test(central_mexico_cumu$covid_rate, listw=rswm_q, zero.policy = TRUE, na.action=na.omit)

## 
##  Moran I test under randomisation
## 
## data:  central_mexico_cumu$covid_rate  
## weights: rswm_q    
## 
## Moran I statistic standard deviate = 11.594, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.531355255      -0.005714286       0.002145937

Computing Monte Carlo Moran’s I

Perform Moran’s I statistic using moran.mc()

set.seed(1234)
central_mexico_moran= moran.mc(central_mexico_cumu$covid_rate, listw=rswm_q, nsim=999, zero.policy = TRUE, na.action=na.omit)
central_mexico_moran

## 
##  Monte-Carlo simulation of Moran I
## 
## data:  central_mexico_cumu$covid_rate 
## weights: rswm_q  
## number of simulations + 1: 1000 
## 
## statistic = 0.53136, observed rank = 1000, p-value = 0.001
## alternative hypothesis: greater

Understand Monte Carklo Moran’s I

mean(central_mexico_moran$res[1:999])

## [1] -0.006679371

var(central_mexico_moran$res[1:999])

## [1] 0.002109503

summary(central_mexico_moran$res[1:999])

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
## -0.139460 -0.039707 -0.009462 -0.006679  0.023299  0.196044

hist(central_mexico_moran$res, freq=TRUE, breaks=50, xlab="Simulated Moran's I")
abline(v=0, col="red") 

fips <- order(central_mexico_cumu$NOMGEO)
localMI <- localmoran(central_mexico_cumu$covid_rate, rswm_q)
head(localMI)

##           Ii         E.Ii    Var.Ii      Z.Ii    Pr(z > 0)
## 270 4.310276 -0.005714286 0.1865610  9.992404 8.227084e-24
## 271 4.012195 -0.005714286 0.1865610  9.302286 6.872897e-21
## 272 2.329954 -0.005714286 0.2345049  4.823200 7.063663e-07
## 273 2.344484 -0.005714286 0.1146451  6.941074 1.945651e-12
## 274 4.443751 -0.005714286 0.1865610 10.301427 3.471191e-25
## 275 2.566689 -0.005714286 0.1146451  7.597336 1.511450e-14

The code chunk below list the content of the local Moran matrix derived by using printCoefmat().

printCoefmat(data.frame(localMI[fips,], row.names=central_mexico_cumu$NOMGEO[fips]), check.names=FALSE)

##                                        Ii        E.Ii      Var.Ii        Z.Ii
## Ã\201lvaro Obregón               2.96790820 -0.00571429  0.13176793  8.19183066
## Acambay de Ruíz Castañeda    0.29904078 -0.00571429  0.23450492  0.62932496
## Acolman                        0.02861044 -0.00571429  0.13176793  0.09455885
## Aculco                         0.61560808 -0.00571429  0.23450492  1.28304240
## Almoloya de Alquisiras         0.59943855 -0.00571429  0.23450492  1.24965201
## Almoloya de Juárez            0.15121531 -0.00571429  0.13176793  0.43231469
## Almoloya del Río              0.55402783 -0.00571429  0.23450492  1.15587803
## Amacuzac                       0.23157634 -0.00571429  0.23450492  0.49000962
## Amanalco                       0.07224975 -0.00571429  0.13176793  0.21477783
## Amatepec                       0.73256751 -0.00571429  0.31441146  1.31665798
## Amecameca                     -0.05186129 -0.00571429  0.23450492 -0.09529443
## Apaxco                         0.28999668 -0.00571429  0.47422455  0.42941323
## Atenco                         0.06936081 -0.00571429  0.15459837  0.19093848
## Atizapán                      0.35129869 -0.00571429  0.31441146  0.63669994
## Atizapán de Zaragoza          0.00013692 -0.00571429  0.15459837  0.01488138
## Atlacomulco                   -0.04151730 -0.00571429  0.18656099 -0.08289134
## Atlatlahucan                   0.21041613 -0.00571429  0.13176793  0.59540301
## Atlautla                       0.18681063 -0.00571429  0.18656099  0.44573478
## Axapusco                       0.00102129 -0.00571429  0.23450492  0.01390910
## Axochiapan                     0.18997812 -0.00571429  0.31441146  0.34899948
## Ayala                          0.19172585 -0.00571429  0.10132734  0.62025762
## Ayapango                       0.07591387 -0.00571429  0.15459837  0.20760487
## Azcapotzalco                   4.31027555 -0.00571429  0.18656099  9.99240419
## Benito Juárez                 2.67217372 -0.00571429  0.15459837  6.81067175
## Calimaya                       0.02840330 -0.00571429  0.11464510  0.10076289
## Capulhuac                     -0.00531959 -0.00571429  0.31441146  0.00070390
## Chalco                         1.13505714 -0.00571429  0.10132734  3.58373017
## Chapa de Mota                  0.55129907 -0.00571429  0.23450492  1.15024309
## Chapultepec                    0.14965968 -0.00571429  0.23450492  0.32085018
## Chiautla                       0.11897926 -0.00571429  0.13176793  0.34350978
## Chicoloapan                    0.00697826 -0.00571429  0.23450492  0.02621034
## Chiconcuac                     0.14218027 -0.00571429  0.31441146  0.26375639
## Chimalhuacán                 -0.00255197 -0.00571429  0.23450492  0.00653025
## Coacalco de Berriozábal       0.07465783 -0.00571429  0.23450492  0.16596992
## Coatepec Harinas               0.53569615 -0.00571429  0.11464510  1.59900149
## Coatetelco                     0.37417095 -0.00571429  0.15459837  0.96616201
## Coatlán del Río              0.30304282 -0.00571429  0.15459837  0.78526187
## Cocotitlán                    0.61523283 -0.00571429  0.31441146  1.10740233
## Coyoacán                      4.01219483 -0.00571429  0.18656099  9.30228600
## Coyotepec                     -0.05408075 -0.00571429  0.23450492 -0.09987765
## Cuajimalpa de Morelos          2.32995440 -0.00571429  0.23450492  4.82319989
## Cuauhtémoc                    4.56733378 -0.00571429  0.15459837 11.63063175
## Cuautitlán                   -0.09161566 -0.00571429  0.11464510 -0.25370110
## Cuautitlán Izcalli           -0.05421215 -0.00571429  0.15459837 -0.12334460
## Cuautla                       -0.08154299 -0.00571429  0.23450492 -0.15658770
## Cuernavaca                    -0.00100731 -0.00571429  0.13176793  0.01296692
## Donato Guerra                  0.43761475 -0.00571429  0.23450492  0.91548282
## Ecatepec de Morelos            0.07801243 -0.00571429  0.08195606  0.29246475
## Ecatzingo                      0.35067183 -0.00571429  0.23450492  0.73594405
## El Oro                        -0.03110005 -0.00571429  0.23450492 -0.05242208
## Emiliano Zapata                0.24545981 -0.00571429  0.15459837  0.63881101
## Gustavo A. Madero              2.34448356 -0.00571429  0.11464510  6.94107395
## Huehuetoca                     0.05875724 -0.00571429  0.23450492  0.13313491
## Hueypoxtla                     0.13972482 -0.00571429  0.31441146  0.25937733
## Huitzilac                     -0.54800341 -0.00571429  0.15459837 -1.37920378
## Huixquilucan                   0.23394186 -0.00571429  0.18656099  0.55485327
## Isidro Fabela                  0.14125433 -0.00571429  0.18656099  0.34026257
## Ixtapaluca                     0.01005285 -0.00571429  0.15459837  0.04010056
## Ixtapan de la Sal              0.48981056 -0.00571429  0.18656099  1.14724194
## Ixtapan del Oro                0.50564595 -0.00571429  0.31441146  0.91196415
## Ixtlahuaca                     0.21464182 -0.00571429  0.18656099  0.51016970
## Iztacalco                      4.44375080 -0.00571429  0.18656099 10.30142684
## Iztapalapa                     2.56668904 -0.00571429  0.11464510  7.59733559
## Jaltenco                      -0.00519974 -0.00571429  0.15459837  0.00130863
## Jantetelco                     0.50140254 -0.00571429  0.23450492  1.04720580
## Jilotepec                      0.43306493 -0.00571429  0.18656099  1.01586412
## Jilotzingo                    -0.00535744 -0.00571429  0.18656099  0.00082617
## Jiquipilco                     0.33330269 -0.00571429  0.15459837  0.86222178
## Jiutepec                       0.22411116 -0.00571429  0.23450492  0.47459388
## Jocotitlán                    0.13908214 -0.00571429  0.13176793  0.39888985
## Jojutla                        0.00355889 -0.00571429  0.23450492  0.01914927
## Jonacatepec de Leandro Valle   0.30008563 -0.00571429  0.23450492  0.63148260
## Joquicingo                     0.15677537 -0.00571429  0.15459837  0.41325990
## Juchitepec                    -0.42497409 -0.00571429  0.10132734 -1.31710347
## La Magdalena Contreras         3.02647316 -0.00571429  0.31441146  5.40762865
## La Paz                        -0.01590005 -0.00571429  0.15459837 -0.02590545
## Lerma                          0.01113800 -0.00571429  0.09067314  0.05596538
## Luvianos                       0.24060635 -0.00571429  0.31441146  0.43929030
## Malinalco                      0.34176524 -0.00571429  0.15459837  0.88374457
## Mazatepec                      0.29519814 -0.00571429  0.15459837  0.76531047
## Melchor Ocampo                 0.12772369 -0.00571429  0.31441146  0.23797440
## Metepec                        0.14490721 -0.00571429  0.13176793  0.41493692
## Mexicaltzingo                  0.28497127 -0.00571429  0.31441146  0.51841107
## Miacatlán                     0.21264204 -0.00571429  0.13176793  0.60153500
## Miguel Hidalgo                 3.38009770 -0.00571429  0.13176793  9.32734352
## Milpa Alta                     4.35750406 -0.00571429  0.11464510 12.88632840
## Morelos                        0.36599237 -0.00571429  0.15459837  0.94536142
## Naucalpan de Juárez           0.45193065 -0.00571429  0.11464510  1.35160849
## Nextlalpan                    -0.06055492 -0.00571429  0.11464510 -0.16196631
## Nezahualcóyotl                0.85686547 -0.00571429  0.11464510  2.54754291
## Nicolás Romero                0.02762146 -0.00571429  0.13176793  0.09183437
## Nopaltepec                     0.01928086 -0.00571429  0.95366381  0.02559517
## Ocoyoacac                     -0.05191146 -0.00571429  0.11464510 -0.13643873
## Ocuilan                        0.19341911 -0.00571429  0.11464510  0.58812054
## Ocuituco                       0.34035674 -0.00571429  0.23450492  0.71464320
## Otumba                        -0.00420795 -0.00571429  0.23450492  0.00311061
## Otzoloapan                     0.40847257 -0.00571429  0.18656099  0.95892777
## Otzolotepec                    0.00663239 -0.00571429  0.15459837  0.03140129
## Ozumba                         0.08780576 -0.00571429  0.13176793  0.25763204
## Papalotla                      0.04531015 -0.00571429  0.31441146  0.09099741
## Polotitlán                    0.71106095 -0.00571429  0.47422455  1.04085678
## Puente de Ixtla               -0.36329394 -0.00571429  0.15459837 -0.90943223
## Rayón                         0.00195686 -0.00571429  0.23450492  0.01584107
## San Antonio la Isla           -0.01017098 -0.00571429  0.15459837 -0.01133470
## San Felipe del Progreso        0.27231213 -0.00571429  0.15459837  0.70710451
## San José del Rincón          0.48112931 -0.00571429  0.23450492  1.00534121
## San Martín de las Pirámides  0.02418816 -0.00571429  0.18656099  0.06923032
## San Mateo Atenco               0.08485207 -0.00571429  0.31441146  0.16151680
## San Simón de Guerrero         0.18375977 -0.00571429  0.31441146  0.33790963
## Santo Tomás                   0.39412857 -0.00571429  0.31441146  0.71308312
## Soyaniquilpan de Juárez       0.27550153 -0.00571429  0.95366381  0.28796659
## Sultepec                       0.70624137 -0.00571429  0.18656099  1.64832377
## Tecámac                      -0.00102663 -0.00571429  0.11464510  0.01384451
## Tejupilco                      0.12300527 -0.00571429  0.13176793  0.35460077
## Temamatla                      0.29675704 -0.00571429  0.18656099  0.70028334
## Temascalapa                   -0.01220166 -0.00571429  0.23450492 -0.01339654
## Temascalcingo                  0.12466398 -0.00571429  0.23450492  0.26923357
## Temascaltepec                  0.35759772 -0.00571429  0.10132734  1.14134363
## Temixco                        0.26666876 -0.00571429  0.18656099  0.63062277
## Temoac                         0.61583049 -0.00571429  0.23450492  1.28350168
## Temoaya                        0.14588144 -0.00571429  0.13176793  0.41762078
## Tenancingo                     0.08693587 -0.00571429  0.15459837  0.23563711
## Tenango del Aire              -0.05866120 -0.00571429  0.18656099 -0.12258299
## Tenango del Valle              0.00590692 -0.00571429  0.10132734  0.03650799
## Teoloyucan                    -0.00057119 -0.00571429  0.23450492  0.01062059
## Teotihuacán                  -0.07271072 -0.00571429  0.15459837 -0.17039200
## Tepalcingo                     0.09674644 -0.00571429  0.23450492  0.21158333
## Tepetlaoxtoc                   0.06525327 -0.00571429  0.13176793  0.19550369
## Tepetlixpa                     0.21161293 -0.00571429  0.18656099  0.50315720
## Tepotzotlán                  -0.01423038 -0.00571429  0.13176793 -0.02346042
## Tepoztlán                    -0.26695541 -0.00571429  0.13176793 -0.71967544
## Tequixquiac                    0.18107619 -0.00571429  0.23450492  0.38572586
## Tetecala                       0.37871645 -0.00571429  0.31441146  0.68559701
## Tetela del Volcán             0.38039574 -0.00571429  0.23450492  0.79732449
## Texcaltitlán                  0.46337238 -0.00571429  0.15459837  1.19302798
## Texcalyacac                   -0.00081996 -0.00571429  0.15459837  0.01244775
## Texcoco                        0.01092783 -0.00571429  0.09067314  0.05526741
## Tezoyuca                       0.02916262 -0.00571429  0.31441146  0.06219976
## Tianguistenco                 -0.15110499 -0.00571429  0.06327661 -0.57798298
## Timilpan                       0.35007483 -0.00571429  0.15459837  0.90487835
## Tláhuac                       6.20913140 -0.00571429  0.18656099 14.38864603
## Tlalmanalco                    0.16232595 -0.00571429  0.13176793  0.46292264
## Tlalnepantla                  -0.32136319 -0.00571429  0.18656099 -0.73079214
## Tlalnepantla de Baz            0.42728487 -0.00571429  0.13176793  1.19283998
## Tlalpan                        3.31291166 -0.00571429  0.10132734 10.42545394
## Tlaltizapán de Zapata         0.13026592 -0.00571429  0.13176793  0.37460263
## Tlaquiltenango                -0.03656745 -0.00571429  0.15459837 -0.07846884
## Tlatlaya                       1.05742465 -0.00571429  0.95366381  1.08866026
## Tlayacapan                     0.05306795 -0.00571429  0.18656099  0.13609296
## Toluca                        -0.03658818 -0.00571429  0.10132734 -0.09699024
## Tonanitla                      0.00443413 -0.00571429  0.18656099  0.02349566
## Tonatico                       0.34435373 -0.00571429  0.47422455  0.50834718
## Totolapan                      0.38245258 -0.00571429  0.18656099  0.89868614
## Tultepec                       0.00812030 -0.00571429  0.18656099  0.03202991
## Tultitlán                     0.00796871 -0.00571429  0.09067314  0.04544038
## Valle de Bravo                 0.00873575 -0.00571429  0.13176793  0.03980743
## Valle de Chalco Solidaridad   -0.44050690 -0.00571429  0.18656099 -1.00663434
## Venustiano Carranza            4.55798281 -0.00571429  0.23450492  9.42412058
## Villa de Allende               0.60030563 -0.00571429  0.23450492  1.25144255
## Villa del Carbón              0.41083129 -0.00571429  0.18656099  0.96438868
## Villa Guerrero                 0.33349008 -0.00571429  0.18656099  0.78532788
## Villa Victoria                 0.48852305 -0.00571429  0.18656099  1.14426109
## Xalatlaco                     -0.00318767 -0.00571429  0.23450492  0.00521751
## Xochimilco                     9.13736680 -0.00571429  0.18656099 21.16811327
## Xochitepec                     0.26122734 -0.00571429  0.18656099  0.61802478
## Xonacatlán                   -0.00443331 -0.00571429  0.23450492  0.00264525
## Xoxocotla                      0.04183113 -0.00571429  0.15459837  0.12092223
## Yautepec                       0.26055911 -0.00571429  0.11464510  0.78641180
## Yecapixtla                     0.26471301 -0.00571429  0.10132734  0.84954658
## Zacatepec                     -0.21438047 -0.00571429  0.23450492 -0.43089960
## Zacazonapan                    0.30498889 -0.00571429  0.18656099  0.71934177
## Zacualpan                      0.82681427 -0.00571429  0.23450492  1.71918716
## Zacualpan de Amilpas           0.52741487 -0.00571429  0.23450492  1.10092175
## Zinacantepec                   0.02149357 -0.00571429  0.15459837  0.06919773
## Zumpahuacán                   0.26555871 -0.00571429  0.15459837  0.68992854
## Zumpango                      -0.00387888 -0.00571429  0.10132734  0.00576592
##                               Pr.z...0.
## Ã\201lvaro Obregón                 0.0000
## Acambay de Ruíz Castañeda      0.2646
## Acolman                          0.4623
## Aculco                           0.0997
## Almoloya de Alquisiras           0.1057
## Almoloya de Juárez              0.3328
## Almoloya del Río                0.1239
## Amacuzac                         0.3121
## Amanalco                         0.4150
## Amatepec                         0.0940
## Amecameca                        0.5380
## Apaxco                           0.3338
## Atenco                           0.4243
## Atizapán                        0.2622
## Atizapán de Zaragoza            0.4941
## Atlacomulco                      0.5330
## Atlatlahucan                     0.2758
## Atlautla                         0.3279
## Axapusco                         0.4945
## Axochiapan                       0.3635
## Ayala                            0.2675
## Ayapango                         0.4178
## Azcapotzalco                     0.0000
## Benito Juárez                   0.0000
## Calimaya                         0.4599
## Capulhuac                        0.4997
## Chalco                           0.0002
## Chapa de Mota                    0.1250
## Chapultepec                      0.3742
## Chiautla                         0.3656
## Chicoloapan                      0.4895
## Chiconcuac                       0.3960
## Chimalhuacán                    0.4974
## Coacalco de Berriozábal         0.4341
## Coatepec Harinas                 0.0549
## Coatetelco                       0.1670
## Coatlán del Río                0.2162
## Cocotitlán                      0.1341
## Coyoacán                        0.0000
## Coyotepec                        0.5398
## Cuajimalpa de Morelos            0.0000
## Cuauhtémoc                      0.0000
## Cuautitlán                      0.6001
## Cuautitlán Izcalli              0.5491
## Cuautla                          0.5622
## Cuernavaca                       0.4948
## Donato Guerra                    0.1800
## Ecatepec de Morelos              0.3850
## Ecatzingo                        0.2309
## El Oro                           0.5209
## Emiliano Zapata                  0.2615
## Gustavo A. Madero                0.0000
## Huehuetoca                       0.4470
## Hueypoxtla                       0.3977
## Huitzilac                        0.9161
## Huixquilucan                     0.2895
## Isidro Fabela                    0.3668
## Ixtapaluca                       0.4840
## Ixtapan de la Sal                0.1256
## Ixtapan del Oro                  0.1809
## Ixtlahuaca                       0.3050
## Iztacalco                        0.0000
## Iztapalapa                       0.0000
## Jaltenco                         0.4995
## Jantetelco                       0.1475
## Jilotepec                        0.1548
## Jilotzingo                       0.4997
## Jiquipilco                       0.1943
## Jiutepec                         0.3175
## Jocotitlán                      0.3450
## Jojutla                          0.4924
## Jonacatepec de Leandro Valle     0.2639
## Joquicingo                       0.3397
## Juchitepec                       0.9061
## La Magdalena Contreras           0.0000
## La Paz                           0.5103
## Lerma                            0.4777
## Luvianos                         0.3302
## Malinalco                        0.1884
## Mazatepec                        0.2220
## Melchor Ocampo                   0.4060
## Metepec                          0.3391
## Mexicaltzingo                    0.3021
## Miacatlán                       0.2737
## Miguel Hidalgo                   0.0000
## Milpa Alta                       0.0000
## Morelos                          0.1722
## Naucalpan de Juárez             0.0883
## Nextlalpan                       0.5643
## Nezahualcóyotl                  0.0054
## Nicolás Romero                  0.4634
## Nopaltepec                       0.4898
## Ocoyoacac                        0.5543
## Ocuilan                          0.2782
## Ocuituco                         0.2374
## Otumba                           0.4988
## Otzoloapan                       0.1688
## Otzolotepec                      0.4875
## Ozumba                           0.3983
## Papalotla                        0.4637
## Polotitlán                      0.1490
## Puente de Ixtla                  0.8184
## Rayón                           0.4937
## San Antonio la Isla              0.5045
## San Felipe del Progreso          0.2398
## San José del Rincón            0.1574
## San Martín de las Pirámides    0.4724
## San Mateo Atenco                 0.4358
## San Simón de Guerrero           0.3677
## Santo Tomás                     0.2379
## Soyaniquilpan de Juárez         0.3867
## Sultepec                         0.0496
## Tecámac                         0.4945
## Tejupilco                        0.3614
## Temamatla                        0.2419
## Temascalapa                      0.5053
## Temascalcingo                    0.3939
## Temascaltepec                    0.1269
## Temixco                          0.2641
## Temoac                           0.0997
## Temoaya                          0.3381
## Tenancingo                       0.4069
## Tenango del Aire                 0.5488
## Tenango del Valle                0.4854
## Teoloyucan                       0.4958
## Teotihuacán                     0.5676
## Tepalcingo                       0.4162
## Tepetlaoxtoc                     0.4225
## Tepetlixpa                       0.3074
## Tepotzotlán                     0.5094
## Tepoztlán                       0.7641
## Tequixquiac                      0.3498
## Tetecala                         0.2465
## Tetela del Volcán               0.2126
## Texcaltitlán                    0.1164
## Texcalyacac                      0.4950
## Texcoco                          0.4780
## Tezoyuca                         0.4752
## Tianguistenco                    0.7184
## Timilpan                         0.1828
## Tláhuac                         0.0000
## Tlalmanalco                      0.3217
## Tlalnepantla                     0.7675
## Tlalnepantla de Baz              0.1165
## Tlalpan                          0.0000
## Tlaltizapán de Zapata           0.3540
## Tlaquiltenango                   0.5313
## Tlatlaya                         0.1382
## Tlayacapan                       0.4459
## Toluca                           0.5386
## Tonanitla                        0.4906
## Tonatico                         0.3056
## Totolapan                        0.1844
## Tultepec                         0.4872
## Tultitlán                       0.4819
## Valle de Bravo                   0.4841
## Valle de Chalco Solidaridad      0.8429
## Venustiano Carranza              0.0000
## Villa de Allende                 0.1054
## Villa del Carbón                0.1674
## Villa Guerrero                   0.2161
## Villa Victoria                   0.1263
## Xalatlaco                        0.4979
## Xochimilco                       0.0000
## Xochitepec                       0.2683
## Xonacatlán                      0.4989
## Xoxocotla                        0.4519
## Yautepec                         0.2158
## Yecapixtla                       0.1978
## Zacatepec                        0.6667
## Zacazonapan                      0.2360
## Zacualpan                        0.0428
## Zacualpan de Amilpas             0.1355
## Zinacantepec                     0.4724
## Zumpahuacán                     0.2451
## Zumpango                         0.4977

local Moran’s

central_mexico.localMI <- cbind(central_mexico_cumu,localMI)

central_moran <- tm_shape(central_mexico.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty",
          palette = "RdBu",
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

Mapping local Moran’s| p-values

tm_shape(central_mexico.localMI) +
  tm_fill(col = "Pr.z...0.", 
          breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
          palette="-Blues", 
          title = "local Moran's I p-values") +
  tm_borders(alpha = 0.5)

Mapping both local Moran’s I values and p-values

From the result, we can analyse that cluster are focused in area Mexico 09.

localMI.map <- tm_shape(central_mexico.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty", 
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

pvalue.map <- tm_shape(central_mexico.localMI) +
  tm_fill(col = "Pr.z...0.", 
          breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
          palette="-Blues", 
          title = "local Moran's I p-values") +
  tm_borders(alpha = 0.5)

tmap_arrange(localMI.map, pvalue.map, asp=1, ncol=2)

Creating LISA clustering Map

The Lisa cluster Map will allow us to understand the spatial autocorrelation. Firstly, I will be using the LISA cluster map to plost Moran Scatterplot.

nci <- moran.plot(central_mexico_cumu$covid_rate, rswm_q, labels=as.character(central_mexico_cumu$NOMGEO), xlab="Covid19 Rate", ylab="Spatially Lag Covid19 Rate")

From the plot, we can observe that high covid 19 rate are clustered in spatially lag convid19 Rate 600-800 to Covid 19 Rate 600 to 800

Plotting Moran scatterplot with standardised variable

central_mexico_cumu$Z.covid_rate <- scale(central_mexico_cumu$covid_rate) %>% as.vector 

nci2 <- moran.plot(central_mexico_cumu$Z.covid_rate, rswm_q, labels=as.character(central_mexico_cumu$NOMGEO), xlab="z-Covid19 Rate", ylab="Spatially Lag z-Covid19 Rate")

that scatter plot is same as the previous scatter plot. From the graph, we can understand that Xochimilco has the hight Cumul rate

Getis and Ord’s G-Statistics

quadrant <- vector(mode="numeric",length=nrow(localMI))
DV <- central_mexico_cumu$covid_rate - mean(central_mexico_cumu$covid_rate)
C_mI <- localMI[,1] - mean(localMI[,1])    
signif <- 0.05       

quadrant[DV >0 & C_mI>0] <- 4      
quadrant[DV <0 & C_mI<0] <- 1      
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3
quadrant[localMI[,5]>signif] <- 0

Cold Spot Area Analysis

central_mexico.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

tm_shape(central_mexico.localMI) +
  tm_fill(col = "quadrant", 
          style = "cat", 
          palette = colors[c(sort(unique(quadrant)))+1], 
          labels = clusters[c(sort(unique(quadrant)))+1]) +
  tm_view(set.zoom.limits = c(11,17)) +
  tm_borders(alpha=0.5)

From the cold spot area analysis, I can identify that the “High-High” area is a region that has higher relative to its surroundings.

Getis and Ord’s G-statistics

Gi statistics using fixed distance

fips <- order(central_mexico$NOMGEO)
gi.adaptive <- localG(central_mexico_cumu$covid_rate, knn_lw)
mexi_combined_cumu.gi <- cbind(central_mexico_cumu, as.matrix(gi.adaptive))
names(mexi_combined_cumu.gi)[29] <- "gstat_adaptive"

tm_shape(mexi_combined_cumu.gi) +
  tm_fill(col = "gstat_adaptive", 
          style = "pretty",
          palette="-RdBu",
          title = "local Gi") +
  tm_borders(alpha = 0.5) + tm_text("NOMGEO", size=0.2) 

From the result above, most of the highlighted areas are in blue and Mexico 09 area tend to have a red colour. This tells me Mexico 09 have higher cluster population than Mexico 15 and 17. Even though Mexico City is small, I can identify that high population lead to high covid 19 rates.

Conclusion

From the Gi Visualisation, the main Covdi19 affected areas are highlighted in red colour. Most of the red areas are from Mexico 09 area. According to the datasets and following visualization, Area (09), Mexico City, has demonstrated a high degree of influence from the COVID-19. As can be seen above, colors describe the weight of GI values and represent whether the highlighted region is a hotspot or a coldspot; red means hotspot, while blue indicates a coldspot. For instance, Area (09) and (15), Mexico City and Mexico State, are indicated as hotspots, due to comparatively higher population in the geographical region than Area (17) - Morelos State. Moreover, Mexico City has the highest population density of the three regions. In other words, there is a correlation between spreading virus and population - and a higher population density can lead to a more critical situation, due to COVID-19.