Take-Home-Ex03

Loading necessary packages

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

## Loading required package: spData

## To access larger datasets in this package, install the spDataLarge
## package with: `install.packages('spDataLarge',
## repos='https://nowosad.github.io/drat/', type='source')`

## Loading required package: sp

## Loading required package: spdep

## Loading required package: sf

## Linking to GEOS 3.8.0, GDAL 3.0.4, PROJ 6.3.1

## Loading required package: rgdal

## rgdal: version: 1.5-17, (SVN revision 1070)
## Geospatial Data Abstraction Library extensions to R successfully loaded
## Loaded GDAL runtime: GDAL 3.0.4, released 2020/01/28
## Path to GDAL shared files: C:/Users/ahhli/OneDrive/Documents/R/win-library/4.0/rgdal/gdal
## GDAL binary built with GEOS: TRUE 
## Loaded PROJ runtime: Rel. 6.3.1, February 10th, 2020, [PJ_VERSION: 631]
## Path to PROJ shared files: C:/Users/ahhli/OneDrive/Documents/R/win-library/4.0/rgdal/proj
## Linking to sp version:1.4-4
## To mute warnings of possible GDAL/OSR exportToProj4() degradation,
## use options("rgdal_show_exportToProj4_warnings"="none") before loading rgdal.

## Loading required package: tmap

## Loading required package: tidyverse

## -- Attaching packages --------------------------------------- tidyverse 1.3.0 --

## v ggplot2 3.3.2     v purrr   0.3.4
## v tibble  3.0.3     v dplyr   1.0.2
## v tidyr   1.1.2     v stringr 1.4.0
## v readr   1.4.0     v forcats 0.5.0

## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

## Loading required package: geobr

## Warning: package 'geobr' was built under R version 4.0.3

## Loading required package: leaflet

## Loading required package: heatmaply

## Loading required package: plotly

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

## Loading required package: viridis

## Loading required package: viridisLite

## 
## ======================
## Welcome to heatmaply version 1.1.1
## 
## Type citation('heatmaply') for how to cite the package.
## Type ?heatmaply for the main documentation.
## 
## The github page is: https://github.com/talgalili/heatmaply/
## Please submit your suggestions and bug-reports at: https://github.com/talgalili/heatmaply/issues
## Or contact: <tal.galili@gmail.com>
## ======================

## Loading required package: psych

## 
## Attaching package: 'psych'

## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha

Load all datasets

brazil_munis <- read.csv("data/BRAZIL_CITIES.csv",sep=";")
# brazil_munis <- st_as_sf(brazil_munis,coords = c("LONG", "LAT"))
list_geobr()

## # A tibble: 23 x 4
##    `function`       geography             years                           source
##    <chr>            <chr>                 <chr>                           <chr> 
##  1 `read_country`   Country               1872, 1900, 1911, 1920, 1933, ~ IBGE  
##  2 `read_region`    Region                2000, 2001, 2010, 2013, 2014, ~ IBGE  
##  3 `read_state`     States                1872, 1900, 1911, 1920, 1933, ~ IBGE  
##  4 `read_meso_regi~ Meso region           2000, 2001, 2010, 2013, 2014, ~ IBGE  
##  5 `read_micro_reg~ Micro region          2000, 2001, 2010, 2013, 2014, ~ IBGE  
##  6 `read_intermedi~ Intermediate region   2017, 2019                      IBGE  
##  7 `read_immediate~ Immediate region      2017, 2019                      IBGE  
##  8 `read_weighting~ Census weighting are~ 2010                            IBGE  
##  9 `read_census_tr~ Census tract (setor ~ 2000, 2010                      IBGE  
## 10 `read_municipal~ Municipality seats (~ 1872, 1900, 1911, 1920, 1933, ~ IBGE  
## # ... with 13 more rows

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

## Using year 2016

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metro <- read_metro_area(year=2016)

## Using year 2016

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Part 0: Data preparation

Metropolitan Regions under São Paulo Macrometropolis: 1. Metropolitan Region of São Paulo 2. Metropolitan Region of Campinas 3. Metropolitan Region of Vale do Paraíba e Litoral Norte 4. Metropolitan Region of Sorocaba 5. Metropolitan Region of Baixada Santista 6. Piracicaba Urban Agglomeration 7. Jundiaí Urban Agglomeration 8. Regional Unit of Bragança Paulista city

According to Wikipedia, there are 174 municipalities.

# Extract munis under all metropolitan regions belonging to São Paulo Macrometropolis
SP_munis <- metro %>%
  select(code_muni,name_muni,abbrev_state, geom) %>%
  filter(abbrev_state == "SP")

additional_munis <- muni %>%
  select(code_muni,name_muni,abbrev_state, geom) %>%
  filter(code_muni %in% c(3504107,3507100,3532405,3538600,3525508,3556354,3507605,3554953,3538204,3536802)) 

final_munis <- rbind(SP_munis,additional_munis)
# Join with all municipalities for more columns 
muni_2016 <- left_join(final_munis, brazil_munis,by=c("name_muni"="CITY"))
# Remove duplicates
muni_2016<-muni_2016[!duplicated(muni_2016$name_muni), ]

After removing the duplicates, we can see from the rstudio environment that there are in total 174 municipalities, which is aligned with the information from wikipedia.

Below is the plot of São Paulo Macrometropolis

qtm(muni_2016)

Proportion of total number of companies under each industry type that is contributed by each municipality level is calculated as shown below.

muni_2016_derived <- muni_2016 %>%
  mutate('INDUSTRY_A' = muni_2016$COMP_A/sum(muni_2016$COMP_A, na.rm = TRUE)) %>%
  mutate('INDUSTRY_B' = muni_2016$COMP_B/sum(muni_2016$COMP_B, na.rm = TRUE)) %>%
  mutate('INDUSTRY_C' = muni_2016$COMP_C/sum(muni_2016$COMP_C, na.rm = TRUE)) %>%
  mutate('INDUSTRY_D' = muni_2016$COMP_D/sum(muni_2016$COMP_D, na.rm = TRUE)) %>%
  mutate('INDUSTRY_E' = muni_2016$COMP_E/sum(muni_2016$COMP_E, na.rm = TRUE)) %>%
  mutate('INDUSTRY_F' = muni_2016$COMP_F/sum(muni_2016$COMP_F, na.rm = TRUE)) %>%
  mutate('INDUSTRY_G' = muni_2016$COMP_G/sum(muni_2016$COMP_G, na.rm = TRUE)) %>%
  mutate('INDUSTRY_H' = muni_2016$COMP_H/sum(muni_2016$COMP_H, na.rm = TRUE)) %>%
  mutate('INDUSTRY_I' = muni_2016$COMP_I/sum(muni_2016$COMP_I, na.rm = TRUE)) %>%
  mutate('INDUSTRY_J' = muni_2016$COMP_J/sum(muni_2016$COMP_J, na.rm = TRUE)) %>%
  mutate('INDUSTRY_K' = muni_2016$COMP_K/sum(muni_2016$COMP_K, na.rm = TRUE)) %>%
  mutate('INDUSTRY_L' = muni_2016$COMP_L/sum(muni_2016$COMP_L, na.rm = TRUE)) %>%
  mutate('INDUSTRY_M' = muni_2016$COMP_M/sum(muni_2016$COMP_M, na.rm = TRUE)) %>%
  mutate('INDUSTRY_N' = muni_2016$COMP_N/sum(muni_2016$COMP_N, na.rm = TRUE)) %>%
  mutate('INDUSTRY_O' = muni_2016$COMP_O/sum(muni_2016$COMP_O, na.rm = TRUE)) %>%
  mutate('INDUSTRY_P' = muni_2016$COMP_P/sum(muni_2016$COMP_P, na.rm = TRUE)) %>%
  mutate('INDUSTRY_Q' = muni_2016$COMP_Q/sum(muni_2016$COMP_Q, na.rm = TRUE)) %>%
  mutate('INDUSTRY_R' = muni_2016$COMP_R/sum(muni_2016$COMP_R, na.rm = TRUE)) %>%
  mutate('INDUSTRY_S' = muni_2016$COMP_S/sum(muni_2016$COMP_S, na.rm = TRUE)) %>%
  mutate('INDUSTRY_T' = muni_2016$COMP_T/sum(muni_2016$COMP_T, na.rm = TRUE)) %>%
  mutate('INDUSTRY_U' = muni_2016$COMP_U/sum(muni_2016$COMP_U, na.rm = TRUE)) %>%
  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)

Part1: Plotting of choropleth maps showing the distribution of spatial specialisation by industry type, 2016 at municipality level.

muni_2016_derived[is.na(muni_2016_derived)] <- 0
A.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_A",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry A for each municipality") + 
  tm_borders(alpha = 0.5) 
B.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_B",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry B for each municipality") + 
  tm_borders(alpha = 0.5) 
C.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_C",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry C for each municipality") + 
  tm_borders(alpha = 0.5) 
D.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_D",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry D for each municipality") + 
  tm_borders(alpha = 0.5) 
E.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_E",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry E for each municipality") + 
  tm_borders(alpha = 0.5) 
F.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_F",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry F for each municipality") + 
  tm_borders(alpha = 0.5) 
G.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_G",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry G for each municipality") + 
  tm_borders(alpha = 0.5) 
H.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_H",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry H for each municipality") + 
  tm_borders(alpha = 0.5) 
I.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_I",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry I for each municipality") + 
  tm_borders(alpha = 0.5) 
J.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_J",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry J for each municipality") + 
  tm_borders(alpha = 0.5) 
K.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_K",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry K for each municipality") + 
  tm_borders(alpha = 0.5) 
L.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_L",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry L for each municipality") + 
  tm_borders(alpha = 0.5) 
M.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_M",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry M for each municipality") + 
  tm_borders(alpha = 0.5) 
N.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_N",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry N for each municipality") + 
  tm_borders(alpha = 0.5) 
O.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_O",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry O for each municipality") + 
  tm_borders(alpha = 0.5) 
P.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_P",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry P for each municipality") + 
  tm_borders(alpha = 0.5) 
Q.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_Q",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry Q for each municipality") + 
  tm_borders(alpha = 0.5) 
R.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_R",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry R for each municipality") + 
  tm_borders(alpha = 0.5) 
S.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_S",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry S for each municipality") + 
  tm_borders(alpha = 0.5) 
T.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_T",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry T for each municipality") + 
  tm_borders(alpha = 0.5) 
U.map <- tm_shape(muni_2016_derived) + 
  tm_fill(col = "INDUSTRY_U",
          n = 5,
          style = "jenks", 
          title = "Proportion of Industry U for each municipality") + 
  tm_borders(alpha = 0.5) 

Tmaps of Industry A,B,C,D:

tmap_mode("plot")

## tmap mode set to plotting

tmap_arrange(A.map, B.map,C.map,D.map, ncol = 2, nrow = 2)

Tmaps of Industry E,F,G,H:

tmap_mode("plot")

## tmap mode set to plotting

tmap_arrange(E.map, F.map,G.map,H.map, ncol = 2, nrow = 2)

Tmaps of Industry I,J,K,L:

tmap_mode("plot")

## tmap mode set to plotting

tmap_arrange(I.map, J.map,K.map,L.map, ncol = 2, nrow = 2)

Tmaps of Industry M,N,O,P:

tmap_mode("plot")

## tmap mode set to plotting

tmap_arrange(M.map, N.map,O.map,P.map, ncol = 2, nrow = 2)

Tmaps of Industry Q,R,S,T:

tmap_mode("plot")

## tmap mode set to plotting

tmap_arrange(Q.map, R.map,S.map,T.map, ncol = 2, nrow = 2)

Tmap of Industry U:

U.map

Based on the choropleth plots above, Industry T is not found in any of the municipalities. Thus, we will remove column “INDUSTRY_T”.

muni_2016_derived <- muni_2016_derived %>%
  select(-INDUSTRY_T)

Part 2: Delineating industry specialisation clusters by using hierarchical clustering method

2.1. Extracting clustering variables

cluster_vars <- muni_2016_derived %>%
  st_set_geometry(NULL)
head(cluster_vars,10)

##               name_muni  INDUSTRY_A  INDUSTRY_B  INDUSTRY_C INDUSTRY_D
## 1              Cabreúva 0.000000000 0.000000000 0.000000000 0.00000000
## 2  Campo Limpo Paulista 0.001685275 0.000000000 0.005041400 0.00000000
## 3               Itupeva 0.004107858 0.009933775 0.009147970 0.02040816
## 4                Jarinu 0.003054561 0.006622517 0.002437233 0.00000000
## 5               Jundiaí 0.000000000 0.000000000 0.000000000 0.00000000
## 6              Louveira 0.003581209 0.000000000 0.004841079 0.00000000
## 7       Várzea Paulista 0.000000000 0.000000000 0.000000000 0.00000000
## 8    Águas De São Pedro 0.000000000 0.000000000 0.000000000 0.00000000
## 9             Analândia 0.000000000 0.000000000 0.000000000 0.00000000
## 10               Araras 0.036128081 0.016556291 0.016059028 0.02040816
##     INDUSTRY_E  INDUSTRY_F  INDUSTRY_G  INDUSTRY_H  INDUSTRY_I  INDUSTRY_J
## 1  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 2  0.001978239 0.004087560 0.003426166 0.002809444 0.003014514 0.003735745
## 3  0.008902077 0.005109450 0.004359217 0.005456805 0.004986974 0.003244200
## 4  0.001978239 0.002205131 0.002224395 0.002809444 0.002642352 0.002654345
## 5  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 6  0.005934718 0.003764858 0.003672491 0.005726944 0.003796055 0.002064491
## 7  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 8  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 9  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 10 0.014836795 0.012531598 0.013555375 0.014533470 0.011164868 0.008454581
##      INDUSTRY_K  INDUSTRY_L  INDUSTRY_M  INDUSTRY_N  INDUSTRY_O  INDUSTRY_P
## 1  0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 2  0.0014478764 0.002501737 0.002869587 0.001840924 0.005813953 0.007145895
## 3  0.0040218790 0.008895066 0.004048168 0.003782721 0.011627907 0.005189281
## 4  0.0008043758 0.001111883 0.001793492 0.001916578 0.005813953 0.003147597
## 5  0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 6  0.0012870013 0.003335650 0.001998463 0.001639179 0.011627907 0.003317737
## 7  0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 8  0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 9  0.0000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 10 0.0098133848 0.009589993 0.009223674 0.007918495 0.011627907 0.009527860
##     INDUSTRY_Q  INDUSTRY_R  INDUSTRY_S INDUSTRY_U
## 1  0.000000000 0.000000000 0.000000000          0
## 2  0.002731518 0.002280502 0.002393776          0
## 3  0.001850383 0.005017104 0.004428486          0
## 4  0.001321702 0.002508552 0.001077199          0
## 5  0.000000000 0.000000000 0.000000000          0
## 6  0.001674156 0.002964652 0.002573309          0
## 7  0.000000000 0.000000000 0.000000000          0
## 8  0.000000000 0.000000000 0.000000000          0
## 9  0.000000000 0.000000000 0.000000000          0
## 10 0.015243634 0.010034208 0.009335727          0

2.1 Data Standardisation

2.1.1 Min-Max standardisation

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

##     INDUSTRY_A  INDUSTRY_B  INDUSTRY_C INDUSTRY_D  INDUSTRY_E  INDUSTRY_F
## 1  0.000000000 0.000000000 0.000000000 0.00000000 0.000000000 0.000000000
## 2  0.001685275 0.000000000 0.005041400 0.00000000 0.001978239 0.004087560
## 3  0.004107858 0.009933775 0.009147970 0.02040816 0.008902077 0.005109450
## 4  0.003054561 0.006622517 0.002437233 0.00000000 0.001978239 0.002205131
## 5  0.000000000 0.000000000 0.000000000 0.00000000 0.000000000 0.000000000
## 6  0.003581209 0.000000000 0.004841079 0.00000000 0.005934718 0.003764858
## 7  0.000000000 0.000000000 0.000000000 0.00000000 0.000000000 0.000000000
## 8  0.000000000 0.000000000 0.000000000 0.00000000 0.000000000 0.000000000
## 9  0.000000000 0.000000000 0.000000000 0.00000000 0.000000000 0.000000000
## 10 0.036128081 0.016556291 0.016059028 0.02040816 0.014836795 0.012531598
##     INDUSTRY_G  INDUSTRY_H  INDUSTRY_I  INDUSTRY_J   INDUSTRY_K  INDUSTRY_L
## 1  0.000000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000000
## 2  0.003426166 0.002809444 0.003014514 0.003735745 0.0014478764 0.002501737
## 3  0.004359217 0.005456805 0.004986974 0.003244200 0.0040218790 0.008895066
## 4  0.002224395 0.002809444 0.002642352 0.002654345 0.0008043758 0.001111883
## 5  0.000000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000000
## 6  0.003672491 0.005726944 0.003796055 0.002064491 0.0012870013 0.003335650
## 7  0.000000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000000
## 8  0.000000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000000
## 9  0.000000000 0.000000000 0.000000000 0.000000000 0.0000000000 0.000000000
## 10 0.013555375 0.014533470 0.011164868 0.008454581 0.0098133848 0.009589993
##     INDUSTRY_M  INDUSTRY_N  INDUSTRY_O  INDUSTRY_P  INDUSTRY_Q  INDUSTRY_R
## 1  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 2  0.002869587 0.001840924 0.005813953 0.007145895 0.002731518 0.002280502
## 3  0.004048168 0.003782721 0.011627907 0.005189281 0.001850383 0.005017104
## 4  0.001793492 0.001916578 0.005813953 0.003147597 0.001321702 0.002508552
## 5  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 6  0.001998463 0.001639179 0.011627907 0.003317737 0.001674156 0.002964652
## 7  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 8  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 9  0.000000000 0.000000000 0.000000000 0.000000000 0.000000000 0.000000000
## 10 0.009223674 0.007918495 0.011627907 0.009527860 0.015243634 0.010034208
##     INDUSTRY_S INDUSTRY_U
## 1  0.000000000          0
## 2  0.002393776          0
## 3  0.004428486          0
## 4  0.001077199          0
## 5  0.000000000          0
## 6  0.002573309          0
## 7  0.000000000          0
## 8  0.000000000          0
## 9  0.000000000          0
## 10 0.009335727          0

row.names(cluster_vars) <- muni_2016_derived$"name_muni"
head(cluster_vars,10)

##                       INDUSTRY_A  INDUSTRY_B  INDUSTRY_C INDUSTRY_D  INDUSTRY_E
## Cabreúva             0.000000000 0.000000000 0.000000000 0.00000000 0.000000000
## Campo Limpo Paulista 0.001685275 0.000000000 0.005041400 0.00000000 0.001978239
## Itupeva              0.004107858 0.009933775 0.009147970 0.02040816 0.008902077
## Jarinu               0.003054561 0.006622517 0.002437233 0.00000000 0.001978239
## Jundiaí              0.000000000 0.000000000 0.000000000 0.00000000 0.000000000
## Louveira             0.003581209 0.000000000 0.004841079 0.00000000 0.005934718
## Várzea Paulista      0.000000000 0.000000000 0.000000000 0.00000000 0.000000000
## Águas De São Pedro   0.000000000 0.000000000 0.000000000 0.00000000 0.000000000
## Analândia            0.000000000 0.000000000 0.000000000 0.00000000 0.000000000
## Araras               0.036128081 0.016556291 0.016059028 0.02040816 0.014836795
##                       INDUSTRY_F  INDUSTRY_G  INDUSTRY_H  INDUSTRY_I
## Cabreúva             0.000000000 0.000000000 0.000000000 0.000000000
## Campo Limpo Paulista 0.004087560 0.003426166 0.002809444 0.003014514
## Itupeva              0.005109450 0.004359217 0.005456805 0.004986974
## Jarinu               0.002205131 0.002224395 0.002809444 0.002642352
## Jundiaí              0.000000000 0.000000000 0.000000000 0.000000000
## Louveira             0.003764858 0.003672491 0.005726944 0.003796055
## Várzea Paulista      0.000000000 0.000000000 0.000000000 0.000000000
## Águas De São Pedro   0.000000000 0.000000000 0.000000000 0.000000000
## Analândia            0.000000000 0.000000000 0.000000000 0.000000000
## Araras               0.012531598 0.013555375 0.014533470 0.011164868
##                       INDUSTRY_J   INDUSTRY_K  INDUSTRY_L  INDUSTRY_M
## Cabreúva             0.000000000 0.0000000000 0.000000000 0.000000000
## Campo Limpo Paulista 0.003735745 0.0014478764 0.002501737 0.002869587
## Itupeva              0.003244200 0.0040218790 0.008895066 0.004048168
## Jarinu               0.002654345 0.0008043758 0.001111883 0.001793492
## Jundiaí              0.000000000 0.0000000000 0.000000000 0.000000000
## Louveira             0.002064491 0.0012870013 0.003335650 0.001998463
## Várzea Paulista      0.000000000 0.0000000000 0.000000000 0.000000000
## Águas De São Pedro   0.000000000 0.0000000000 0.000000000 0.000000000
## Analândia            0.000000000 0.0000000000 0.000000000 0.000000000
## Araras               0.008454581 0.0098133848 0.009589993 0.009223674
##                       INDUSTRY_N  INDUSTRY_O  INDUSTRY_P  INDUSTRY_Q
## Cabreúva             0.000000000 0.000000000 0.000000000 0.000000000
## Campo Limpo Paulista 0.001840924 0.005813953 0.007145895 0.002731518
## Itupeva              0.003782721 0.011627907 0.005189281 0.001850383
## Jarinu               0.001916578 0.005813953 0.003147597 0.001321702
## Jundiaí              0.000000000 0.000000000 0.000000000 0.000000000
## Louveira             0.001639179 0.011627907 0.003317737 0.001674156
## Várzea Paulista      0.000000000 0.000000000 0.000000000 0.000000000
## Águas De São Pedro   0.000000000 0.000000000 0.000000000 0.000000000
## Analândia            0.000000000 0.000000000 0.000000000 0.000000000
## Araras               0.007918495 0.011627907 0.009527860 0.015243634
##                       INDUSTRY_R  INDUSTRY_S INDUSTRY_U
## Cabreúva             0.000000000 0.000000000          0
## Campo Limpo Paulista 0.002280502 0.002393776          0
## Itupeva              0.005017104 0.004428486          0
## Jarinu               0.002508552 0.001077199          0
## Jundiaí              0.000000000 0.000000000          0
## Louveira             0.002964652 0.002573309          0
## Várzea Paulista      0.000000000 0.000000000          0
## Águas De São Pedro   0.000000000 0.000000000          0
## Analândia            0.000000000 0.000000000          0
## Araras               0.010034208 0.009335727          0

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.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.005333   Median :0.00000   Median :0.007727   Median :0.00000  
##  Mean   :0.048501   Mean   :0.06676   Mean   :0.060463   Mean   :0.03129  
##  3rd Qu.:0.036000   3rd Qu.:0.07692   3rd Qu.:0.052072   3rd Qu.:0.00000  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.000000   Max.   :1.00000  
##    INDUSTRY_E        INDUSTRY_F         INDUSTRY_G         INDUSTRY_H     
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.000000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.003922   Median :0.006185   Median :0.00462  
##  Mean   :0.05235   Mean   :0.046560   Mean   :0.049603   Mean   :0.04468  
##  3rd Qu.:0.05180   3rd Qu.:0.043355   3rd Qu.:0.042456   3rd Qu.:0.03349  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.000000   Max.   :1.00000  
##    INDUSTRY_I         INDUSTRY_J        INDUSTRY_K          INDUSTRY_L       
##  Min.   :0.000000   Min.   :0.00000   Min.   :0.0000000   Min.   :0.0000000  
##  1st Qu.:0.000000   1st Qu.:0.00000   1st Qu.:0.0000000   1st Qu.:0.0000000  
##  Median :0.005657   Median :0.00142   Median :0.0009852   Median :0.0008475  
##  Mean   :0.051389   Mean   :0.03320   Mean   :0.0351962   Mean   :0.0350429  
##  3rd Qu.:0.037604   3rd Qu.:0.01931   3rd Qu.:0.0174877   3rd Qu.:0.0177966  
##  Max.   :1.000000   Max.   :1.00000   Max.   :1.0000000   Max.   :1.0000000  
##    INDUSTRY_M        INDUSTRY_N         INDUSTRY_O       INDUSTRY_P      
##  Min.   :0.00000   Min.   :0.000000   Min.   :0.0000   Min.   :0.000000  
##  1st Qu.:0.00000   1st Qu.:0.000000   1st Qu.:0.0000   1st Qu.:0.000000  
##  Median :0.00250   Median :0.001948   Median :0.1429   Median :0.003647  
##  Mean   :0.03115   Mean   :0.036990   Mean   :0.1412   Mean   :0.044799  
##  3rd Qu.:0.01465   3rd Qu.:0.015338   3rd Qu.:0.2143   3rd Qu.:0.036141  
##  Max.   :1.00000   Max.   :1.000000   Max.   :1.0000   Max.   :1.000000  
##    INDUSTRY_Q         INDUSTRY_R         INDUSTRY_S         INDUSTRY_U      
##  Min.   :0.000000   Min.   :0.000000   Min.   :0.000000   Min.   :0.000000  
##  1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.000000  
##  Median :0.001449   Median :0.003067   Median :0.004407   Median :0.000000  
##  Mean   :0.031494   Mean   :0.038652   Mean   :0.042325   Mean   :0.008621  
##  3rd Qu.:0.015331   3rd Qu.:0.029141   3rd Qu.:0.031952   3rd Qu.:0.000000  
##  Max.   :1.000000   Max.   :1.000000   Max.   :1.000000   Max.   :1.000000

2.2.2 Z-score standardisation

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

##            vars   n mean sd median trimmed  mad   min   max range  skew
## INDUSTRY_A    1 174    0  1  -0.36   -0.25 0.07 -0.41  7.96  8.37  4.77
## INDUSTRY_B    2 174    0  1  -0.52   -0.21 0.00 -0.52  7.29  7.81  3.71
## INDUSTRY_C    3 174    0  1  -0.38   -0.25 0.08 -0.44  6.80  7.23  3.86
## INDUSTRY_D    4 174    0  1  -0.25   -0.22 0.00 -0.25  7.78  8.03  6.08
## INDUSTRY_E    5 174    0  1  -0.42   -0.24 0.00 -0.42  7.68  8.11  4.59
## INDUSTRY_F    6 174    0  1  -0.36   -0.24 0.05 -0.40  8.13  8.53  4.83
## INDUSTRY_G    7 174    0  1  -0.36   -0.23 0.08 -0.42  7.95  8.37  4.81
## INDUSTRY_H    8 174    0  1  -0.31   -0.22 0.05 -0.35  7.48  7.84  5.52
## INDUSTRY_I    9 174    0  1  -0.38   -0.24 0.07 -0.42  7.81  8.23  4.48
## INDUSTRY_J   10 174    0  1  -0.30   -0.23 0.02 -0.32  9.22  9.53  5.94
## INDUSTRY_K   11 174    0  1  -0.30   -0.23 0.01 -0.30  8.32  8.62  5.76
## INDUSTRY_L   12 174    0  1  -0.32   -0.24 0.01 -0.33  9.12  9.45  5.74
## INDUSTRY_M   13 174    0  1  -0.29   -0.23 0.04 -0.32  9.82 10.13  6.49
## INDUSTRY_N   14 174    0  1  -0.29   -0.22 0.02 -0.31  8.06  8.37  5.80
## INDUSTRY_O   15 174    0  1   0.01   -0.15 1.32 -0.88  5.37  6.25  1.95
## INDUSTRY_P   16 174    0  1  -0.36   -0.23 0.05 -0.40  8.45  8.85  5.16
## INDUSTRY_Q   17 174    0  1  -0.30   -0.22 0.02 -0.31  9.55  9.86  6.45
## INDUSTRY_R   18 174    0  1  -0.35   -0.23 0.04 -0.38  9.35  9.72  5.81
## INDUSTRY_S   19 174    0  1  -0.33   -0.23 0.06 -0.37  8.45  8.82  5.32
## INDUSTRY_U   20 174    0  1  -0.10   -0.10 0.00 -0.10 11.72 11.83 10.39
##            kurtosis   se
## INDUSTRY_A    28.67 0.08
## INDUSTRY_B    19.72 0.08
## INDUSTRY_C    17.40 0.08
## INDUSTRY_D    41.45 0.08
## INDUSTRY_E    26.82 0.08
## INDUSTRY_F    29.47 0.08
## INDUSTRY_G    28.80 0.08
## INDUSTRY_H    34.62 0.08
## INDUSTRY_I    25.27 0.08
## INDUSTRY_J    43.76 0.08
## INDUSTRY_K    38.29 0.08
## INDUSTRY_L    41.79 0.08
## INDUSTRY_M    53.77 0.08
## INDUSTRY_N    38.67 0.08
## INDUSTRY_O     6.44 0.08
## INDUSTRY_P    33.78 0.08
## INDUSTRY_Q    50.80 0.08
## INDUSTRY_R    44.59 0.08
## INDUSTRY_S    34.64 0.08
## INDUSTRY_U   112.12 0.08

2.3.Computing proximity matrix using euclidean distance

cluster_vars.std_df <- as.data.frame(cluster_vars.std)
proxmat <- dist(cluster_vars.std_df, method = 'euclidean')

2.4. Computing hierarchical clustering

Hierarchical cluster analysis using ward.D method

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

groups <- as.factor(cutree(hclust_ward, k=6))

muni_2016_cluster <- cbind(muni_2016_derived, as.matrix(groups)) %>%
  rename('CLUSTER'='as.matrix.groups.')
qtm(muni_2016_cluster, "CLUSTER")

Part 3: Spatially Constrained Clustering

Convert muni_2016_derived sf into a SpatialPolygonDataFrame, muni_2016_sp

muni_2016_sp <- as_Spatial(muni_2016_derived)

## Warning in showSRID(uprojargs, format = "PROJ", multiline = "NO", prefer_proj =
## prefer_proj): Discarded datum Unknown based on GRS80 ellipsoid in CRS definition

## Warning in showSRID(SRS_string, format = "PROJ", multiline = "NO", prefer_proj
## = prefer_proj): Discarded datum Sistema de Referencia Geocentrico para las
## AmericaS 2000 in CRS definition

muni_2016_sp

## class       : SpatialPolygonsDataFrame 
## features    : 174 
## extent      : -48.40857, -44.16137, -24.492, -22.01305  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +ellps=GRS80 +no_defs 
## variables   : 21
## names       :          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, ... 
## min values  : Águas De São Pedro,                 0,                  0,                  0,                 0,                 0,                 0,                 0,                 0,                 0,                 0,                 0,                 0,                 0,                 0, ... 
## max values  :         Votorantim, 0.118495892142406, 0.0860927152317881, 0.0950520833333333, 0.183673469387755, 0.109792284866469, 0.123433550260851, 0.115862624935619, 0.128640121022205, 0.111834759955341, 0.173122296500197, 0.163288288288288, 0.164002779708131, 0.184473481936972, 0.155368941342614, ...

Compute the neighbours list from polygon list using poly2nd() of spdep package

muni_2016.nb <- poly2nb(muni_2016_sp)
summary(muni_2016.nb)

## Neighbour list object:
## Number of regions: 174 
## Number of nonzero links: 882 
## Percentage nonzero weights: 2.913199 
## Average number of links: 5.068966 
## 1 region with no links:
## 100
## Link number distribution:
## 
##  0  1  2  3  4  5  6  7  8  9 10 22 
##  1  4 13 23 36 31 29 16  9  6  5  1 
## 4 least connected regions:
## 8 9 29 36 with 1 link
## 1 most connected region:
## 161 with 22 links

By using the boundary map, we plot the neighbours list. The neighbour list contains coordinates which are used to extract the centroids of each polygon.

plot(muni_2016_sp, border=grey(.5))
plot(muni_2016.nb, coordinates(muni_2016_sp), col="blue", add=TRUE)

Using the SKATER method, the new clusters are plotted as shown below: As you can observe from the new clusters, the clusters gained from SKATER method are relatively fragmented.

muni2016_sf_spatialcluster <- cbind(muni_2016_cluster, as.factor(groups))
qtm(muni2016_sf_spatialcluster,'CLUSTER')