The centered ternary balance scheme: A technique to visualize surfaces of unbalanced three-part compositions

Jonas Schöley

Read the paper: 10.4054/DemRes.2021.44.19

BACKGROUND : The ternary balance scheme is a visualization technique that encodes three-part compositions as a mixture of three primary colors. The technique works best if the compositional data are well spread out across the domain but fails to show structure in very unbalanced data.

OBJECTIVE : I extend the ternary balance scheme such that it can be utilized to show variation in unbalanced compositional surfaces.

METHODS : By reprojecting an unbalanced compositional data set around its center of location and visualizing the transformed data with a standard ternary balance scheme, the internal variation of the data becomes visible. An appropriate centering operation has been defined within the field of compositional data analysis.

RESULTS : Using Europe's regional workforce structure by economic sector as an example, I have demonstrated the utility of the centered ternary balance scheme in visualizing variation across unbalanced compositional surfaces.

CONTRIBUTION : I have proposed a technique to visualize the internal variation in surfaces of highly unbalanced compositional data and implemented it in the tricolore R package.

Code

• code/01-download_euro_data: Download geodata for European NUTS-2 regions and associated statistics on workforce and educational attainment.
• code/02-create_euro_basemap: Create a flat map of Europe.
• code/03-create_figures: Create figures featured in paper.

Data

Eurostat data, downloaded on March 5, 2020.

• data/euro_education.csv: Relative share of population ages 25 to 64 by educational attainment in the European NUTS-2 regions 2016. Data derived from Eurostat table "edat_lfse_04", downloaded on March 5, 2020.
  • id: NUTS-2 code
  • ed_0to2: Share of population with highest attained education "lower secondary or less".
  • ed_3to4: Share of population with highest attained education "upper secondary".
  • ed_5to8: Share of population with highest attained education "tertiary".
• data/euro_sectors.csv: Relative share of workers by labor-force sector in the European NUTS-2 regions 2016. The original NACE (rev. 2) codes have been recoded into the three sectors "primary" (A), "secondary" (B-E & F) and "tertiary" (all other NACE codes). Data derived from Eurostat table "lfst_r_lfe2en2", downloaded on March 5, 2020.
  • id: NUTS-2 code
  • lf_pri: Share of labor-force in primary sector.
  • lf_sec: Share of labor-force in secondary sector.
  • lf_ter: Share of labor-force in tertiary sector.
• data/euro_geo_nuts2.RData: A simple-features dataframe containing the NUTS-2 level polygons of European regions. Derived from Eurostat European Geodata. (c) EuroGeographics for the administrative boundaries (http://ec.europa.eu/eurostat/web/gisco/geodata/reference-data/administrative-units-statistical-units/), downloaded on March 5, 2020.
  • id: NUTS-2 code.
  • name: Name of NUTS-2 region.
  • geometry: Polygon outlines for regions in sf package format.
• data/euro_basemap.RData: A ggplot object representing a simple map of Europe.