Harvey Lauw

Note: Recommend to use Navigation bar on the left as code chunkz may be too long for scrolling.

Overview

Objectives

Brazil is the world’s fifth-largest country by area and the sixth most populous. Brazil is classified as an upper-middle income economy by the World Bank and a developing country, with the largest share of global wealth in Latin America. It is considered an advanced emerging economy.

It has the ninth largest GDP in the world by nominal, and eighth by PPP measures. Behind all this impressive figures, the spatial development of Brazil is highly unequal as shown in the figure on the right. In 2016, the GDP per capita of the poorest municipality is R$3,190.6. On the other hand, the GDP per capita of the richest municipality is R$314,638. Half of the municipalities have GDP per capita less than R$16,000 and the top 25% municipalities earn R$26,155 and above.

Installing and Launching R Packages

packages = c('spData','sp','spdep','rgdal', 'tmap', 'sf', 'ggpubr', 'cluster', 'factoextra', 'NbClust', 'heatmaply', 'corrplot', 'psych', 'tidyverse','geobr','leaflet')
for (p in packages){
  if(!require(p, character.only = T)){
    install.packages(p)
    }
  library(p,character.only = T)
}

Importing data

# Import csv file with ";" as delimiter
brazil <- read.csv("data/aspatial/BRAZIL_CITIES.csv",sep=";", fileEncoding = "UTF-8")

Initial Data preparation and Analysis

Preparing a series of choropleth maps showing the distribution of spatial specialisation by industry type, 2016 at municipality level.

Referencing to https://en.wikipedia.org/wiki/Greater_S%C3%A3o_Paulo#Metropolitan_Area for the list of Municipals listed under São Paulo Macrometropolis.

Download Sao Paulo’s State Boundary with geobr package.

municipalities <- read_municipality(code_muni = "SP",year=2016)

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# 1st area of study area
metro <- read_metro_area(year=2016)

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Data Wrangling

a <- metro %>%
  filter(name_metro %in% c("RM São Paulo","RM Campinas","RM do Vale do Paraíba e Litoral Norte","RM de Sorocaba","RM Baixada Santista"
)) %>%
  select(code_muni,name_muni,geom)

# 2nd area of study area
b <- municipalities %>%
  filter(code_muni %in% c(3512209,3503307,3526704,3512704,3502002,3543907,3546702,3512407,3526902,3521408,3521101,3511706,3550407,3500600,3547007,3538709,3526407,3545159,3544004,3530904,3542107,3510401,3514908,3509601,3556503,3525904,3508405,3524006,3525201,3527306,3504107,3507100,3532405,3538600,3525508,3556354,3507605,3554953,3538204,3536802,3545803)) %>%
  select(code_muni,name_muni,geom)



municipalities_metro <- rbind(a,b)

municipalities_2016 <- inner_join(municipalities_metro, brazil, by=c("name_muni"="CITY"))

municipalities_2016 <- municipalities_2016[!duplicated(municipalities_2016$name_muni),] %>%
  filter(name_muni != "Ilhabela")

municipalities <- municipalities_2016 %>%
  mutate(INDUSTRY_A = (`COMP_A`/`COMP_TOT`)/(sum(municipalities_2016$COMP_A)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_B = (`COMP_B`/`COMP_TOT`)/(sum(municipalities_2016$COMP_B)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_C = (`COMP_C`/`COMP_TOT`)/(sum(municipalities_2016$COMP_C)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_D = (`COMP_D`/`COMP_TOT`)/(sum(municipalities_2016$COMP_D)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_E = (`COMP_E`/`COMP_TOT`)/(sum(municipalities_2016$COMP_E)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_F = (`COMP_F`/`COMP_TOT`)/(sum(municipalities_2016$COMP_F)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_G = (`COMP_G`/`COMP_TOT`)/(sum(municipalities_2016$COMP_G)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_H = (`COMP_H`/`COMP_TOT`)/(sum(municipalities_2016$COMP_H)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_I = (`COMP_I`/`COMP_TOT`)/(sum(municipalities_2016$COMP_I)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_J = (`COMP_J`/`COMP_TOT`)/(sum(municipalities_2016$COMP_J)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_K = (`COMP_K`/`COMP_TOT`)/(sum(municipalities_2016$COMP_K)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_L = (`COMP_L`/`COMP_TOT`)/(sum(municipalities_2016$COMP_L)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_M = (`COMP_M`/`COMP_TOT`)/(sum(municipalities_2016$COMP_M)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_N = (`COMP_N`/`COMP_TOT`)/(sum(municipalities_2016$COMP_N)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_O = (`COMP_O`/`COMP_TOT`)/(sum(municipalities_2016$COMP_O)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_P = (`COMP_P`/`COMP_TOT`)/(sum(municipalities_2016$COMP_P)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_Q = (`COMP_Q`/`COMP_TOT`)/(sum(municipalities_2016$COMP_Q)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_R = (`COMP_R`/`COMP_TOT`)/(sum(municipalities_2016$COMP_R)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_S = (`COMP_S`/`COMP_TOT`)/(sum(municipalities_2016$COMP_S)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_T = (`COMP_T`/`COMP_TOT`)/(sum(municipalities_2016$COMP_T)/max(municipalities_2016$COMP_TOT))) %>%
  mutate(INDUSTRY_U = (`COMP_U`/`COMP_TOT`)/(sum(municipalities_2016$COMP_U)/max(municipalities_2016$COMP_TOT))) %>%
  select(name_muni,INDUSTRY_A,INDUSTRY_B,INDUSTRY_C,INDUSTRY_D,INDUSTRY_E,INDUSTRY_F,INDUSTRY_G,INDUSTRY_H,INDUSTRY_I,INDUSTRY_J,INDUSTRY_K,INDUSTRY_L,INDUSTRY_M,INDUSTRY_N,INDUSTRY_O,INDUSTRY_P,INDUSTRY_Q,INDUSTRY_R,INDUSTRY_S,INDUSTRY_T,INDUSTRY_U)

summary(municipalities)

##               name_muni     INDUSTRY_A        INDUSTRY_B        INDUSTRY_C    
##  Águas De São Pedro:  1   Min.   : 0.0000   Min.   : 0.0000   Min.   :0.0000  
##  Alambari          :  1   1st Qu.: 0.1901   1st Qu.: 0.0000   1st Qu.:0.3387  
##  Alumínio          :  1   Median : 0.8660   Median : 0.6622   Median :0.5222  
##  Americana         :  1   Mean   : 3.3712   Mean   : 2.7310   Mean   :0.5841  
##  Analândia         :  1   3rd Qu.: 3.5002   3rd Qu.: 2.4727   3rd Qu.:0.7722  
##  Aparecida         :  1   Max.   :29.7301   Max.   :43.7013   Max.   :1.7339  
##  (Other)           :166                                                       
##    INDUSTRY_D        INDUSTRY_E       INDUSTRY_F       INDUSTRY_G    
##  Min.   : 0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.1168  
##  1st Qu.: 0.0000   1st Qu.:0.2977   1st Qu.:0.3097   1st Qu.:0.4931  
##  Median : 0.0000   Median :0.5529   Median :0.4307   Median :0.5486  
##  Mean   : 0.3215   Mean   :0.7086   Mean   :0.4268   Mean   :0.5435  
##  3rd Qu.: 0.0000   3rd Qu.:0.9321   3rd Qu.:0.5289   3rd Qu.:0.6107  
##  Max.   :22.5329   Max.   :6.4510   Max.   :0.9418   Max.   :1.0212  
##                                                                      
##    INDUSTRY_H       INDUSTRY_I       INDUSTRY_J       INDUSTRY_K     
##  Min.   :0.0000   Min.   :0.1376   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.3392   1st Qu.:0.4366   1st Qu.:0.1008   1st Qu.:0.09858  
##  Median :0.4694   Median :0.5046   Median :0.1557   Median :0.15833  
##  Mean   :0.5549   Mean   :0.5677   Mean   :0.2114   Mean   :0.17669  
##  3rd Qu.:0.6760   3rd Qu.:0.6205   3rd Qu.:0.2254   3rd Qu.:0.23289  
##  Max.   :1.8737   Max.   :1.7086   Max.   :3.7974   Max.   :1.02792  
##                                                                      
##    INDUSTRY_L       INDUSTRY_M       INDUSTRY_N       INDUSTRY_O     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   : 0.1331  
##  1st Qu.:0.1314   1st Qu.:0.1633   1st Qu.:0.1517   1st Qu.: 0.6314  
##  Median :0.2718   Median :0.2312   Median :0.2450   Median : 1.4798  
##  Mean   :0.2762   Mean   :0.2525   Mean   :0.2731   Mean   : 3.4316  
##  3rd Qu.:0.3756   3rd Qu.:0.3142   3rd Qu.:0.3438   3rd Qu.: 3.5807  
##  Max.   :0.8744   Max.   :1.1689   Max.   :1.2493   Max.   :64.2167  
##                                                                      
##    INDUSTRY_P       INDUSTRY_Q       INDUSTRY_R       INDUSTRY_S     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.05842  
##  1st Qu.:0.3265   1st Qu.:0.1745   1st Qu.:0.3354   1st Qu.:0.33040  
##  Median :0.4815   Median :0.2696   Median :0.4429   Median :0.42679  
##  Mean   :0.4707   Mean   :0.2878   Mean   :0.4190   Mean   :0.43197  
##  3rd Qu.:0.6276   3rd Qu.:0.3686   3rd Qu.:0.5397   3rd Qu.:0.51544  
##  Max.   :1.0403   Max.   :0.8595   Max.   :0.8986   Max.   :1.13592  
##                                                                      
##    INDUSTRY_T    INDUSTRY_U                 geom    
##  Min.   : NA   Min.   :0.00000   MULTIPOLYGON :172  
##  1st Qu.: NA   1st Qu.:0.00000   epsg:4674    :  0  
##  Median : NA   Median :0.00000   +proj=long...:  0  
##  Mean   :NaN   Mean   :0.02169                      
##  3rd Qu.: NA   3rd Qu.:0.00000                      
##  Max.   : NA   Max.   :2.04474                      
##  NA's   :172

qtm(municipalities_2016 )

Exploratory Spatial Data Analysis

As seen from the summary of the municipalities above, Industry_T will be removed as it only has NA values for all 173 municipalities in the extended metropolitan of Sao Paulo.

Going by how the individual Histogram have turned out for each industry types, majority of the industry specialization are left skewed.

municipalities_2016 <- municipalities %>%
  select(-INDUSTRY_T)

options(scipen=999)
ggplot_A <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_A`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_B <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_B`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_C <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_C`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_D <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_D`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_E <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_E`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_F <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_F`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_G <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_G`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_H <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_H`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_I <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_I`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_J <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_J`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_K <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_K`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_L <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_L`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_M <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_M`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_N <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_N`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_O <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_O`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_P <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_P`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_Q <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_Q`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_R <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_R`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_S <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_S`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_U <- ggplot(data=municipalities_2016, aes(x=`INDUSTRY_U`)) +
  geom_histogram(bins=10, color="black", fill="light blue")

ggarrange(ggplot_A, ggplot_B, ggplot_C, ggplot_D, 
          ggplot_E, ggplot_F, ggplot_G, ggplot_H, 
          ggplot_I, ggplot_J, ncol = 4, nrow = 3)

ggarrange(ggplot_K, ggplot_L, ggplot_M, ggplot_N, 
          ggplot_O, ggplot_P, ggplot_Q, ggplot_R, 
          ggplot_S, ggplot_U, ncol = 4, nrow = 3)

After plotting the choropleth maps for each industry with the same scale below, we can see that the distribution of specialisation in Industry A (Agriculture, livestock, forestry, fishing and aquaculture), B (Extractive Industries) & O (Public administration, defense and social security) are more prominent and has more contribution in terms of specialization value than the rest of the industry types.

tmap_mode("plot")
map_A <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_A",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_B <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_B",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_C <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_C",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

map_D <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_D",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_E <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_E",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_F <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_F",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_G <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_G",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_H <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_H",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

map_I <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_I",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_J <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_J",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

map_K <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_K",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_L <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_L",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_M <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_M",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

map_N <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_N",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_O <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_O",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_P <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_P",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_Q <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_Q",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_R <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_R",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

map_S <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_S",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5) 

map_U <- tm_shape(municipalities_2016) + 
  tm_fill(col = "INDUSTRY_U",
          breaks = c(0,3,6,9,12,Inf),
          style = "fixed") + 
  tm_borders(alpha = 0.5)

tmap_mode("plot")
tmap_arrange(map_A, map_B, map_C, map_D, map_E, ncol = 2, nrow = 3)

tmap_arrange(map_F, map_G, map_H, map_I, map_J, ncol = 2, nrow = 3)

tmap_arrange(map_K, map_L, map_M, map_N, map_O, ncol = 2, nrow = 3)

tmap_arrange(map_P, map_Q, map_R, map_S, map_U, ncol = 2, nrow = 3)

Hierarchical Clustering

Delineating industry specialisation clusters by using hierarchical clustering method and display their distribution by using appropriate thematic mapping technique.

Data wrangling for Hierarchical clustering

cluster_vars <- municipalities_2016 %>%
  st_set_geometry(NULL)

# Data wrangling on cluster df to retain municipalities name in the df index rows insead
row.names(cluster_vars) <- cluster_vars$"name_muni"

cluster_vars <- select(cluster_vars, c(2:21))
head(cluster_vars,10)

##              INDUSTRY_A INDUSTRY_B INDUSTRY_C INDUSTRY_D INDUSTRY_E INDUSTRY_F
## Bertioga     0.06000187 0.00000000  0.1461699  0.0000000  0.6624576  0.5628240
## Cubatão      0.00000000 0.00000000  0.2259147  0.7162923  0.9164473  0.7981820
## Guarujá      0.09238128 0.00000000  0.1709507  0.0000000  0.2677359  0.4784058
## Itanhaém     0.24053208 0.00000000  0.2140999  0.0000000  0.9294679  0.4125952
## Mongaguá     0.09790340 0.81648278  0.1345393  0.0000000  1.0809140  0.8248094
## Peruíbe      0.09466101 0.00000000  0.1773867  0.0000000  0.4703022  0.4377991
## Praia Grande 0.01483465 0.00000000  0.1769861  0.0000000  0.4585943  0.6931762
## Santos       0.06805407 0.43657611  0.1605539  0.0000000  0.3583404  0.3314533
## São Vicente  0.01301904 0.32572374  0.2061510  0.0000000  0.8624293  0.4698228
## Americana    0.07481783 0.08508498  0.9323449  0.0000000  0.8110162  0.4731829
##              INDUSTRY_G INDUSTRY_H INDUSTRY_I INDUSTRY_J INDUSTRY_K INDUSTRY_L
## Bertioga      0.4717020  0.0824820  0.8730414 0.10421058 0.13684431  0.6358968
## Cubatão       0.5102022  1.2691384  0.7677175 0.10787891 0.12677085  0.1256719
## Guarujá       0.4805127  0.2108984  0.6971338 0.09168387 0.09876140  0.3337678
## Itanhaém      0.6907332  0.2302735  1.0756262 0.12930463 0.06857171  0.4518943
## Mongaguá      0.5525454  0.1634230  0.8756210 0.06477621 0.00000000  0.5093552
## Peruíbe       0.7099187  0.2370160  1.0235280 0.09394639 0.14167801  0.3967250
## Praia Grande  0.4597898  0.1849896  0.6019971 0.10305861 0.10361326  0.4259148
## Santos        0.3663554  0.7766790  0.5705721 0.27535665 0.28504675  0.3823043
## São Vicente   0.5311062  0.3106358  0.7572859 0.15504906 0.15309989  0.2859848
## Americana     0.5413902  0.3375981  0.4712196 0.22782175 0.28358307  0.6919991
##              INDUSTRY_M INDUSTRY_N INDUSTRY_O INDUSTRY_P INDUSTRY_Q INDUSTRY_R
## Bertioga      0.1410770  1.1133804  1.2342632  0.3073978  0.2094547  0.5660469
## Cubatão       0.3032053  0.3453129  1.6261772  0.6234953  0.3104579  0.7043507
## Guarujá       0.1679967  1.1665901  0.4750803  0.4296903  0.2398481  0.5567971
## Itanhaém      0.1590585  0.2850620  1.2369610  0.6080324  0.2518950  0.5672842
## Mongaguá      0.1150957  0.8552946  1.3426090  0.6863625  0.1822728  0.2394527
## Peruíbe       0.1669259  0.3197292  1.4604121  0.5551532  0.3221819  0.6201494
## Praia Grande  0.1456214  1.2492556  0.2034366  0.3959997  0.1881516  0.4561250
## Santos        0.4347948  0.9821937  0.4307385  0.4015831  0.5896444  0.5340937
## São Vicente   0.2318745  0.6771243  0.5356140  0.6608400  0.2476856  0.6345663
## Americana     0.3994012  0.3727549  0.3497804  0.4208987  0.3632697  0.5204517
##              INDUSTRY_S INDUSTRY_U
## Bertioga      0.4292224  0.0000000
## Cubatão       0.5728572  0.0000000
## Guarujá       0.4521874  0.0000000
## Itanhaém      0.5809961  0.0000000
## Mongaguá      0.2728638  0.0000000
## Peruíbe       0.4748886  0.0000000
## Praia Grande  0.3721071  0.0000000
## Santos        0.5417798  0.3710897
## São Vicente   0.8418119  0.0000000
## Americana     0.3601755  0.0000000

Viewing Min-max & Z-score standardization data frames

#normalizing all columns into the same scale
cluster_vars.std <- normalize(cluster_vars)
summary(cluster_vars.std)

##    INDUSTRY_A         INDUSTRY_B        INDUSTRY_C       INDUSTRY_D     
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.006395   1st Qu.:0.00000   1st Qu.:0.1953   1st Qu.:0.00000  
##  Median :0.029129   Median :0.01515   Median :0.3012   Median :0.00000  
##  Mean   :0.113393   Mean   :0.06249   Mean   :0.3368   Mean   :0.01427  
##  3rd Qu.:0.117733   3rd Qu.:0.05658   3rd Qu.:0.4453   3rd Qu.:0.00000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.0000   Max.   :1.00000  
##    INDUSTRY_E        INDUSTRY_F       INDUSTRY_G       INDUSTRY_H    
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.04615   1st Qu.:0.3288   1st Qu.:0.4161   1st Qu.:0.1810  
##  Median :0.08571   Median :0.4573   Median :0.4775   Median :0.2505  
##  Mean   :0.10984   Mean   :0.4531   Mean   :0.4719   Mean   :0.2961  
##  3rd Qu.:0.14449   3rd Qu.:0.5616   3rd Qu.:0.5462   3rd Qu.:0.3608  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##    INDUSTRY_I       INDUSTRY_J        INDUSTRY_K       INDUSTRY_L    
##  Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.1903   1st Qu.:0.02653   1st Qu.:0.0959   1st Qu.:0.1503  
##  Median :0.2336   Median :0.04099   Median :0.1540   Median :0.3109  
##  Mean   :0.2737   Mean   :0.05566   Mean   :0.1719   Mean   :0.3159  
##  3rd Qu.:0.3074   3rd Qu.:0.05936   3rd Qu.:0.2266   3rd Qu.:0.4295  
##  Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.0000  
##    INDUSTRY_M       INDUSTRY_N       INDUSTRY_O         INDUSTRY_P    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.000000   Min.   :0.0000  
##  1st Qu.:0.1397   1st Qu.:0.1214   1st Qu.:0.007775   1st Qu.:0.3139  
##  Median :0.1978   Median :0.1961   Median :0.021014   Median :0.4629  
##  Mean   :0.2160   Mean   :0.2186   Mean   :0.051472   Mean   :0.4525  
##  3rd Qu.:0.2688   3rd Qu.:0.2752   3rd Qu.:0.053798   3rd Qu.:0.6033  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.000000   Max.   :1.0000  
##    INDUSTRY_Q       INDUSTRY_R       INDUSTRY_S       INDUSTRY_U     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.2031   1st Qu.:0.3733   1st Qu.:0.2524   1st Qu.:0.00000  
##  Median :0.3136   Median :0.4928   Median :0.3419   Median :0.00000  
##  Mean   :0.3349   Mean   :0.4663   Mean   :0.3467   Mean   :0.01061  
##  3rd Qu.:0.4288   3rd Qu.:0.6006   3rd Qu.:0.4241   3rd Qu.:0.00000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000

cluster_vars.z <- scale(cluster_vars)
describe(cluster_vars.z)

##            vars   n mean sd median trimmed  mad   min   max range  skew
## INDUSTRY_A    1 172    0  1  -0.44   -0.25 0.20 -0.59  4.59  5.18  2.51
## INDUSTRY_B    2 172    0  1  -0.39   -0.24 0.18 -0.51  7.63  8.14  3.82
## INDUSTRY_C    3 172    0  1  -0.19   -0.08 0.89 -1.76  3.47  5.23  0.80
## INDUSTRY_D    4 172    0  1  -0.18   -0.16 0.00 -0.18 12.21 12.38 10.74
## INDUSTRY_E    5 172    0  1  -0.19   -0.15 0.63 -0.88  7.09  7.97  3.68
## INDUSTRY_F    6 172    0  1   0.02   -0.01 0.90 -2.28  2.75  5.03  0.10
## INDUSTRY_G    7 172    0  1   0.04    0.04 0.68 -3.44  3.85  7.29 -0.32
## INDUSTRY_H    8 172    0  1  -0.24   -0.14 0.67 -1.56  3.71  5.27  1.43
## INDUSTRY_I    9 172    0  1  -0.24   -0.15 0.54 -1.64  4.34  5.97  2.04
## INDUSTRY_J   10 172    0  1  -0.16   -0.15 0.25 -0.62 10.48 11.10  7.60
## INDUSTRY_K   11 172    0  1  -0.13   -0.09 0.69 -1.27  6.11  7.37  2.10
## INDUSTRY_L   12 172    0  1  -0.02   -0.05 1.06 -1.54  3.34  4.88  0.46
## INDUSTRY_M   13 172    0  1  -0.15   -0.10 0.74 -1.73  6.29  8.02  2.04
## INDUSTRY_N   14 172    0  1  -0.14   -0.14 0.73 -1.39  4.96  6.35  2.25
## INDUSTRY_O   15 172    0  1  -0.31   -0.20 0.25 -0.53  9.78 10.31  6.11
## INDUSTRY_P   16 172    0  1   0.05   -0.01 1.09 -2.31  2.80  5.11  0.09
## INDUSTRY_Q   17 172    0  1  -0.11   -0.07 0.85 -1.69  3.36  5.05  0.81
## INDUSTRY_R   18 172    0  1   0.13    0.06 0.82 -2.26  2.58  4.84 -0.46
## INDUSTRY_S   19 172    0  1  -0.03   -0.05 0.82 -2.24  4.23  6.47  0.81
## INDUSTRY_U   20 172    0  1  -0.12   -0.12 0.00 -0.12 11.53 11.66  9.84
##            kurtosis   se
## INDUSTRY_A     6.42 0.08
## INDUSTRY_B    20.34 0.08
## INDUSTRY_C     0.46 0.08
## INDUSTRY_D   126.44 0.08
## INDUSTRY_E    20.05 0.08
## INDUSTRY_F    -0.10 0.08
## INDUSTRY_G     2.40 0.08
## INDUSTRY_H     2.08 0.08
## INDUSTRY_I     5.30 0.08
## INDUSTRY_J    70.99 0.08
## INDUSTRY_K     9.13 0.08
## INDUSTRY_L    -0.05 0.08
## INDUSTRY_M     8.93 0.08
## INDUSTRY_N     7.31 0.08
## INDUSTRY_O    52.06 0.08
## INDUSTRY_P    -0.15 0.08
## INDUSTRY_Q     0.86 0.08
## INDUSTRY_R     0.19 0.08
## INDUSTRY_S     2.04 0.08
## INDUSTRY_U   104.39 0.08

Observing Min-Max standardization score standardization of specialization values by different industry types.

cluster_vars.std_df <- as.data.frame(cluster_vars.std)

ggplot_A.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_A`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_B.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_B`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_C.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_C`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_D.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_D`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_E.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_E`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_F.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_F`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_G.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_G`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_H.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_H`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_I.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_I`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_J.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_J`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_K.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_K`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_L.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_L`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_M.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_M`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_N.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_N`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_O.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_O`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_P.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_P`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_Q.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_Q`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_R.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_R`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_S.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_S`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_U.std <- ggplot(data=cluster_vars.std_df, aes(x=`INDUSTRY_U`)) +
  geom_histogram(bins=10, color="black", fill="light blue")

ggarrange(ggplot_A.std, ggplot_B.std, ggplot_C.std, ggplot_D.std, 
          ggplot_E.std, ggplot_F.std, ggplot_G.std, ggplot_H.std, 
          ggplot_I.std, ggplot_J.std, ncol = 4, nrow = 3)

ggarrange(ggplot_K.std, ggplot_L.std, ggplot_M.std, ggplot_N.std, 
          ggplot_O.std, ggplot_P.std, ggplot_Q.std, ggplot_R.std, 
          ggplot_S.std, ggplot_U.std, ncol = 4, nrow = 3)

Observing Z-score standardization of specialization values by different industry types.

cluster_vars.z_df <- as.data.frame(cluster_vars.z)

ggplot_A.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_A`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_B.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_B`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_C.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_C`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_D.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_D`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_E.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_E`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_F.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_F`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_G.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_G`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_H.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_H`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_I.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_I`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_J.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_J`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_K.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_K`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_L.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_L`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_M.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_M`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_N.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_N`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_O.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_O`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_P.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_P`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_Q.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_Q`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_R.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_R`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_S.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_S`)) +
  geom_histogram(bins=10, color="black", fill="light blue")
ggplot_U.z <- ggplot(data=cluster_vars.z_df, aes(x=`INDUSTRY_U`)) +
  geom_histogram(bins=10, color="black", fill="light blue")

ggarrange(ggplot_A.z, ggplot_B.z, ggplot_C.z, ggplot_D.z, 
          ggplot_E.z, ggplot_F.z, ggplot_G.z, ggplot_H.z, 
          ggplot_I.z, ggplot_J.z, ncol = 4, nrow = 3)

ggarrange(ggplot_K.z, ggplot_L.z, ggplot_M.z, ggplot_N.z, 
          ggplot_O.z, ggplot_P.z, ggplot_Q.z, ggplot_R.z, 
          ggplot_S.z, ggplot_U.z, ncol = 4, nrow = 3)

Selecting the optimal clustering algorithm

Majority of the industry’s specialization values are not normal distributed, Hence, Z-score standardisation will not be used in this study.

Comparing the 2 types of standardization before choosing on one of them to be used for clustering. Standardization of of variables is performed as the specialization values for every industry types as some industries such as Industry A(Agriculture, livestock, forestry, fishing and aquaculture), B(Extractive Industries) & O(Public administration, defense and social security) can go up to a specialization value of 29,43 & 63 respectively from the summary done in the earlier stage of data analysis above.

Hence, we will use Min-Max Standardisation for this variable as the values range of the clustering variables is large. the ward method will be used for this clustering method as it provides the strongest clustering structure among the four methods assessed with the value of 0.9166987.

proxmat <- dist(cluster_vars.std_df, method = 'euclidean')

m <- c( "average", "single", "complete", "ward")
names(m) <- c( "average", "single", "complete", "ward")

ac <- function(x) {
  agnes(cluster_vars.std_df, method = x)$ac
}

map_dbl(m, ac)

##   average    single  complete      ward 
## 0.7231876 0.6774261 0.7870491 0.9140459

Gap Statistic Method

With reference to the gap statistic graph above, the recommended number of cluster to retain is 19 with the vertical dotted line. However, it doesn’t make sense to retain 19 cluster which does not provide much insight as the map visualizations become too fragmented. Since gap statistic was inconclusive, elbow method & silhouette method is also performed to derive a common optimal number of cluster. For all these 3 methods, the hcut function will be used instead of kmeans to get a more standardized comparison.

The silhouette’s result on the recommended number of cluster to retain is 2 with the vertical dotted line is too small and the next peak on the graph are 6 clusters.Additionally, basing off Within sum-of-square values in the Elbow method, we can safely choose 6-7 clusters. In conclusion, 6 cluster is chosen for this study.

Due to the number of municipalities taken into account as well as the nature of hierarchical cluster analysis method, the cluster 6 became very fragmented. Therefore a further need to perform spatial clustering algorithm is required.

set.seed(12345)
gap_stat <- clusGap(cluster_vars.std_df, FUN = hcut, nstart = 25, K.max = 20, B = 50)
# Print the result
print(gap_stat, method = "firstmax")

## Clustering Gap statistic ["clusGap"] from call:
## clusGap(x = cluster_vars.std_df, FUNcluster = hcut, K.max = 20,     B = 50, nstart = 25)
## B=50 simulated reference sets, k = 1..20; spaceH0="scaledPCA"
##  --> Number of clusters (method 'firstmax'): 20
##           logW   E.logW       gap      SE.sim
##  [1,] 3.699753 4.369021 0.6692674 0.008950965
##  [2,] 3.599271 4.315819 0.7165486 0.008187479
##  [3,] 3.553173 4.283646 0.7304728 0.007819323
##  [4,] 3.517790 4.258480 0.7406898 0.007917840
##  [5,] 3.469169 4.236786 0.7676170 0.007854791
##  [6,] 3.430929 4.217656 0.7867270 0.008153492
##  [7,] 3.390177 4.199629 0.8094520 0.008292550
##  [8,] 3.365923 4.182496 0.8165735 0.008360539
##  [9,] 3.337953 4.166167 0.8282141 0.008598510
## [10,] 3.314654 4.150672 0.8360178 0.008589883
## [11,] 3.289819 4.135442 0.8456234 0.008739370
## [12,] 3.270656 4.120712 0.8500554 0.008668046
## [13,] 3.245447 4.106383 0.8609362 0.008552189
## [14,] 3.225107 4.092359 0.8672515 0.008347481
## [15,] 3.206219 4.078702 0.8724835 0.008391128
## [16,] 3.183868 4.065288 0.8814203 0.008508669
## [17,] 3.159863 4.052097 0.8922339 0.008514621
## [18,] 3.143274 4.039258 0.8959846 0.008597857
## [19,] 3.126591 4.026468 0.8998778 0.008652558
## [20,] 3.109562 4.013847 0.9042855 0.008700016

fviz_gap_stat(gap_stat)

fviz_nbclust(cluster_vars.std_df, hcut, method = "silhouette")

fviz_nbclust(cluster_vars.std_df, hcut, method = "wss")

Viewing the clusters using a dendogram

hclust_ward <- hclust(proxmat, method = 'ward.D')
plot(hclust_ward, cex = 0.6)
rect.hclust(hclust_ward, k = 6, border = 2:5)

groups <- as.factor(cutree(hclust_ward, k=6))
municipalities_2016_cluster <- cbind(municipalities_2016, as.matrix(groups)) %>%
  rename(`CLUSTER`=`as.matrix.groups.`)
qtm(municipalities_2016_cluster, "CLUSTER")

Spatially Constrained Clustering

Delineating industry specialisation clusters by using spatially constrained clustering method and display their distribution by using appropriate thematic mapping technique.

Data Wrangling for Spatially Constrained clustering

municipalities_2016_sp <- as_Spatial(municipalities_2016)
municipalities_2016_5641 <- spTransform(municipalities_2016_sp ,
                          CRS("+init=epsg:5641"))

municipalities_2016.nb <- poly2nb(municipalities_2016_5641)
summary(municipalities_2016.nb)

## Neighbour list object:
## Number of regions: 172 
## Number of nonzero links: 866 
## Percentage nonzero weights: 2.927258 
## Average number of links: 5.034884 
## Link number distribution:
## 
##  1  2  3  4  5  6  7  8  9 10 22 
##  4 13 24 36 32 29 14  9  6  4  1 
## 4 least connected regions:
## 6 133 134 168 with 1 link
## 1 most connected region:
## 129 with 22 links

Observing links between each municipalities.

plot(municipalities_2016_5641, border=grey(.5),main="São Paulo Macrometropolis")
plot(municipalities_2016.nb, coordinates(municipalities_2016_5641), col="Red", add=TRUE)

Computing minimum spanning tree

lcosts <- nbcosts(municipalities_2016.nb, cluster_vars.z_df)
municipalities_2016.w <- nb2listw(municipalities_2016.nb, lcosts, style="B")
summary(municipalities_2016.w)

## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 172 
## Number of nonzero links: 866 
## Percentage nonzero weights: 2.927258 
## Average number of links: 5.034884 
## Link number distribution:
## 
##  1  2  3  4  5  6  7  8  9 10 22 
##  4 13 24 36 32 29 14  9  6  4  1 
## 4 least connected regions:
## 6 133 134 168 with 1 link
## 1 most connected region:
## 129 with 22 links
## 
## Weights style: B 
## Weights constants summary:
##     n    nn       S0       S1       S2
## B 172 29584 4324.106 54370.96 642323.1

municipalities_2016.mst <- mstree(municipalities_2016.w)


plot(municipalities_2016_sp, border=gray(.5))
plot.mst(municipalities_2016.mst, coordinates(municipalities_2016_sp), 
     col="red", cex.lab=0.7, cex.circles=0.005, add=TRUE)

clust6 <- skater(municipalities_2016.mst[,1:2], cluster_vars.std_df, method = "euclidean", 5)

ccs6 <- clust6$groups

plot(municipalities_2016_sp, border=gray(.5))
plot(clust6, coordinates(municipalities_2016_sp), cex.lab=.7,
     groups.colors=c("red","green","blue","pink","yellow","black"), 
     cex.circles=0.005, add=TRUE)

groups_mat <- as.matrix(clust6$groups)
municipalities_2016_spatialcluster <- cbind(municipalities_2016_cluster, as.factor(groups_mat)) %>% rename(`SP_CLUSTER`=`as.factor.groups_mat.`)

qtm(municipalities_2016_spatialcluster, "SP_CLUSTER")

Comparison between hierarchical & spatially constrained Clustering.

The clear distinction would be that with spatially constained clustering, the clusters generated do not get fragmented and will be grouped together. As we can make a direct inference from the spatially constained clusters as well. As compared with Hierarchical clustering where there different municipalities in different clusters but they’re still side by side or even within each clusters as shown below on the left.

Although in this study we could not use gap statistic to determine the optimal number of cluster, but with the help of elbow method as well as silhouette method, the outcome of spatially constrained clustering are much clearer and more readable that that on the left which is the outcome of hierachical clustering.

From the Spatially constrained clustering choropleth, we can see that the main cluster in orange is centered around the Metropolitan Region of Sao Paulo which segments of Metropolitan region of Campinas, Metropolitan tegion of Baixada Santista, Jundaiai Urban Agglomeration & Regional Unit of Braganca Paulista city. This can be proven by the ranking in the number of population in each Region as well from the highest to the least: - Metropolitan Region of Sao Paulo - Metropolitan Region of Campinas - Metropolitan Region of Vale do Paraíba e Litoral Norte - Metropolitan Region of Sorocaba - Metropolitan Region of Baixada Santista - Piracicaba Urban Agglomeration - Jundiaí Urban Agglomeration - Regional Unit of Bragança Paulista city

tmap_mode("view")
hclust.map <- qtm(municipalities_2016_cluster,
                  "CLUSTER") + 
  tm_borders(alpha = 0.5) +
  tm_basemap(server = "http://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png")

shclust.map <- qtm(municipalities_2016_spatialcluster,
                   "SP_CLUSTER") + 
  tm_borders(alpha = 0.5) +
  tm_basemap(server = "http://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png")

tmap_arrange(hclust.map, shclust.map,ncol=2, sync = TRUE)

IS415-Geospatial Analytics and Applications: Take Home Ex3