1. Introducing case-study and MTA
1.1 Multiscalar Territorial Analysis for Policy Study
Beginning in the MTA conceptual framework, several issues must be considered: the study area, the territorial hierarchy and the selected indicator.
Metropolis of Greater Paris (MGP) : a study area making sense in a political context.
The MGP has been created the 1st January 2016 after a preparatory mission and aims at finding solutions to improve and develop the potential of the Paris metropolitan area to be more present at international level (following the initiatives that took place in London, New-York or Tokyo). The official website (last visit: 2022-06) of this infrastructure provides all the details of this new level of governance. Namely, this spatial planning project proposes to “develop a stronger solidarity between territories, reduce territorial inequalities and propose a rebalancing in term of access to household, employment, training, services and amenities”. For this emerging zoning of spatial planning, the need for indicators and analysis of territorial inequalities is high. The MTA methodology seems to be particularly adapted to propose territorial evidences in this context.From the IRIS to the MGP, a lot of hierarchical territorial divisions are available.
The lowest territorial level existing in France associated with public statistical information is IRIS (Ilots Regroupés pour l’Information Statistique). The reference size targeted for each IRIS is 2000 inhabitants (last visit: 2022-06). Each municipality over 10 000 inhabitants and a high proportion of municipalities between 5 000 and 10 000 inhabitants are split in IRIS. It is possible to merge these IRIS in municipalities (36 000 territorial units in France). These municipalities can also be aggregated in Établissements Publics Territoriaux(equivalent to Établissement de Coopération intercommunale, EPCI) or in départements. Each territorial context has specific competences in spatial planning term. Thus, the MGP is constituted by a large number of territorial divisions. It allows the calculation of a high number of deviations according to these territorial contexts. This analysis is mainly focused on municipalities and Établissements Publics Territoriaux (EPT) but could be extended to other territorial levels.Indicators relevant at this scale of analysis.
The chosen indicator (average income tax reference per households) is one of the key drivers of spatial planning policies at local level in France. It is one of the indicators considered relevant for city policy (Politique de la Ville, last visit: 2022-06).
This vignette proposes some concrete outputs for improving the knowledge on income inequalities and proposing solutions for a better geographical distribution of wealth in the MGP area. Relevant statistics will be computed using MTA functionalities and plotted on graphics and maps.
1.2 Dataset and complementary Packages
The example dataset, GrandParisMetropole includes all the required information to create
com is a sf object. It includes the geometries, identifiers (DEPCOM) and names (LIBCOM) of the 150 MGP municipalities identifiers and names of the EPT of belonging of each municipality (EPT and LIB_EPT), identifier of the département of belonging of each municipality (DEP) and the statistical indicators for the multiscalar inequality analysis, the numerator (amount of income tax references in Euros, INC) and the denominator (number of tax households, TH) (see ?com).
EPT is a sf object. It includes the geometries of the 12 EPT of the MGP (see ?EPT).
cardist is a matrix including the a time distance matrix between municipalities computed using
osrmpackage (see ?cardist).
Two additional packages are used: mapsf for thematic mapping purposes and ineq for computing inequality indexes and Lorenz Curve Plot.
# load packages
library(sf)## Linking to GEOS 3.9.0, GDAL 3.2.2, PROJ 7.2.1; sf_use_s2() is TRUElibrary(MTA)
library(mapsf)
library(ineq)
# load dataset
com <- st_read(system.file("metroparis.gpkg", package = "MTA"),
layer = "com", quiet = TRUE)
ept <- st_read(system.file("metroparis.gpkg", package = "MTA"),
layer = "ept", quiet = TRUE)
# set row names to municipalities names
row.names(com) <- com$LIBCOM1.3 Context Maps
Context maps highlight the territorial organization of the study area and provide some first insights regarding the spatial patterns introduced by the indicator used for the analysis.
1.3.1 Study Area
The 150 municipalities of the MGP belongs to 12 intermediate territorial divisions: the Établissements Publics Territoriaux (EPT). This territorial zoning follows approximately the delineation of the départements : Seine-Saint-Denis (in blue on the map below); Paris (in purple); Hauts-de-Seine (in green) and _Val-de-Marine (in orange).
# label / colors management
LIBEPT <- c("Paris", "Est Ensemble", "Grand-Paris Est",
"Territoire des aeroports", "Plaine Commune", "Boucle Nord 92",
"La Defense","Grand Paris Sud Ouest", "Sud Hauts-de-Seine",
"Val de Bievres - Seine Amond - Grand Orly",
"Plaine Centrale - Haut Val-de-Marne - Plateau Briard",
"Association des Communes de l'Est Parisien")
# colors
cols <- c("#cfcfcf", # Grey(Paris)
"#92C8E0", "#7BB6D3", "#64A4C5", "#458DB3", # Blues (dept 93)
"#A6CC99", "#8CBB80", "#71A966", "#4E9345", # Greens (dept 92)
"#F38F84", "#EF6860", "#EA3531") # Reds (dept 94)
colEpt <- data.frame(LIBEPT, cols)
# zoning
mf_map(x = com, var="LIBEPT", type = "typo",
val_order = LIBEPT, pal = cols, lwd = 0.2, border = "white",
leg_pos = "left", leg_title = "EPT of belonging")
mf_map(ept, col = NA, border = "black", add = TRUE)
# layout
mf_layout(title = "Territorial Zoning of the MGP",
credits = paste0("Sources : GEOFLA® 2015 v2.1, Apur, impots.gouv.fr",
"\nRonan Ysebaert, RIATE, 2021"))
1.3.2 Map numerator and denominator
The numerator (number of tax households) and the denominator (total amount of income tax references) building the reference ratio (average income per tax households) are firstly plotted.
# layout
opar <- par(mfrow = c(1, 2))
# numerator map
com$INCM <- com$INC / 1000000
mf_map(com, col = "peachpuff", border = NA)
mf_map(ept, col = NA, border = "black", add = TRUE)
mf_map(x = com, var = "INCM", type = "prop",
col = "#F6533A", inches = 0.15, border = "white",
leg_pos = "topleft", leg_val_rnd = 0,
leg_title = "Amount of income taxe reference\n(millions of euros)")
# layout
mf_layout(title = "Numerator - Amount of income tax reference",
credits = paste0("Sources : GEOFLA® 2015 v2.1, Apur, impots.gouv.fr",
"\nRonan Ysebaert, RIATE, 2021"),
arrow = FALSE)
# denominator map
mf_map(com, col = "peachpuff", border = NA)
mf_map(ept, col = NA, border = "black", add = TRUE)
mf_map(x = com, var = "TH", type = "prop",
col = "#515FAA", inches = 0.15, border = "white",
leg_pos = "topleft", leg_val_rnd = -2,
leg_title = "Number of tax households", add = TRUE)
# layout
mf_layout(title = "Denominator - Tax households",
credits = paste0("Sources : GEOFLA® 2015 v2.1, Apur, impots.gouv.fr",
"\nRonan Ysebaert, RIATE, 2021"),
arrow = FALSE)
par(opar)
Without surprise, the highest amounts of tax households and income are located in the central area of the MGP (Parisian Arrondissements). That being said, these two maps suggest an unequal distribution of income when looking at the distribution of population in Paris suburbs.
1.3.3 Ratio
# ratio
com$ratio <- com$INC / com$TH
# ratio map
mf_map(x = com, var = "ratio", type = "choro",
breaks = c(min(com$ratio, na.rm = TRUE),
20000, 30000, 40000, 50000, 60000,
max(com$ratio, na.rm = TRUE)),
pal = c("#FCDACA", "#F6A599", "#F07168", "#E92B28", "#C70003", "#7C000C"),
border = "white", lwd = 0.2, leg_pos = "topleft", leg_val_rnd = 0,
leg_title = paste0("Average amount of income tax",
"\nreference per households\n(in euros)"))
# EPT borders
mf_map(ept, col = NA, border = "black", add = TRUE)
# Label min and max
mf_label(x = com[which.min(com$ratio),], var = "LIBCOM", cex = 0.6, font = 2,
halo = TRUE)
mf_label(x = com[which.max(com$ratio),], var = "LIBCOM", cex = 0.6, font = 2,
halo = TRUE)
# layout
mf_layout(title = "Ratio - Income per tax households, 2013",
credits = paste0("Sources : GEOFLA® 2015 v2.1, Apur, impots.gouv.fr",
"\nRonan Ysebaert, RIATE, 2021"),
arrow = FALSE)
The MGP area is characterized by high income inequalities. For the 150 municipalities of this area, the values extend from 14 730 (La Courneuve) to 96 310 euros (Paris_7th Arrondissement). 53 municipalities of the MGP area (35 % of the municipalities) are below the French average, i.e. 25 660 euros. The lagging households are mainly concentrated into the north part of MGP area. Highest values are concentrated in the Western part of Paris and its suburbs.
1.4 Introducing the MTA Functions
1.4.1 General, territorial and spatial deviations
MTA package introduces three contexts to monitor territorial inequalities: the general, the territorial and the spatial deviations.
The global deviation is dedicated to the analysis of inequalities using a value of reference. In this example the global deviation refers to the inequalities existing between each municipality in regard to the whole MGP average.
The territorial deviation consists in measuring the inequalities existing for each basic territorial unit as regards to an intermediate territorial level of reference. In this case-study, it will be the EPT of belonging of each municipality. It implies to include beforehand in the input dataset a territorial level of belong for each territorial unit.
The spatial deviation is a measure of inequalities taking into account the neighborhood as a reference. It allows to measure the deviation existing between basic territorial units using three possible parameters : the territorial contiguity (order 1, 2 or n), the spatial neighborhood (territorial units located at less than X kilometers) or functional distances (territorial units located at less than Y minutes by road for instance). In MTA, territorial contiguity and spatial neighborhood measures are directly calculated. Functional distances must be uploaded separately through a dataframe structured with the following fields : id1, id2, distance measure. For this case-study, the contiguity criteria (order 1) will be used for the calculation of the spatial deviation. It gives a good proxy of proximity relationships according to the size and the homogeneity of the municipalities of the MGP area. Other measures could be also adapted, such as time-distances by road (municipalities located at less than 15 minutes by car) or by public transportation.
1.4.2 Relative and absolute deviations
In MTA, two methods are implemented to measure statistical differences to a given context of reference: a relative deviation and an absolute deviation. In MTA, each indicator is considered as a ratio defined by a numerator (GDP for instance) divided by a denominator (population for instance).
The relative deviation states the position of each region as regards to a reference context. It is based on the following calculation: Relative deviation (Region i) = 100 * ((Numerator(Region i)/Denominator(Region i)) /(reference ratio)) Territorial units characterized by a context of reference below index 100 are under the average of a given reference context, and reciprocally.
The absolute deviation specifies which process of redistribution should be realized in absolute terms to achieve a perfect equilibrium for the ratio of reference in the global, the territorial or the spatial context. It is calculated as below: Absolute deviation (Region i) = Numerator (Region i) - (reference ratio * denominator (Region i)) In concrete terms, it examines how much amount of the numerator should be moved in order to reach equidistribution, for each territorial unit, taking into account as a reference the selected deviation context value. More generally, absolute deviation must be considered as a statistical tool to discuss on the amplitude of existing territorial inequalities. It is obvious that reaching a perfect equilibrium between territorial units is highly sensitive and is scarcely a policy objective itself. It is nevertheless interesting to consider the amount of money or population affected by the inequality to have in hand a concrete material for leading discussions on this delicate spatial planning issue.
1.4.3 Cartography of relative and absolute deviations
In this vignette, color palette proposed for displaying on map the relative deviations are the ones suggested by the HyperAtlas tool (blue palette = under the average; red palette = above the average). But other diverging palettes (green/red, etc.) could be also be used for displaying MTA results on maps.
Absolute deviations are highlighted using proportional circles on maps. It examines which amount of the numerator should be moved to the poorest municipalities to reach equidistribution. Circles displayed in a red means that the territorial unit have to contribute a given amount of numerator to achieve the equilibrium in a given context; and reciprocally blue circles means that the territorial unit have to receive frmo the others.
It is quite easy to reproduce or adapt these maps using the functions proposed by the mapsf package.
1.4.4 Synthesis
The analysis of the three deviations provides generally a lot of information. The synthesis functions bidev and mst helps to summarize values of the global, territorial and spatial deviations and allow to answer to some basic and interesting questions:
- Which territorial units are positioned in a favorable/lagging situation for 2 or 3 deviations?
- Which territorial units are positioned in a contradictory situations ? This is especially interesting from a social and policy points of view (NIMBY phenomena, characterizing the opposition by residents to a proposal for a new development because it is close to them).
Moreover, some additional functions are implemented to ease the mapping (map_bidev and map_mst) or proposing appropriate plots (plot_bidev and plot_mst) for visualizing these results.
