Visualizing compositional data on the Lexis surface

Abstract

Background: The Lexis surface plot is an established visualization tool in demography. Its presentutility, however, is limited to the domain of one-dimensional magnitudes such as ratesand counts. Visualizing proportions among three or more groups on a period-age grid isan unsolved problem. Objective: We seek to extend the Lexis surface plot to the domain of compositional data. Methods: We propose four techniques for visualizing group compositions on a period-age grid. Todemonstrate the techniques we use data on age-specific cause-of-death compositions inFrance from 1925 to 1999. We compare the visualizations for compliance with multipledesired criteria. Results: Compositional data can effectively be visualized on the Lexis surface. A key feature ofthe classical Lexis surface plot - to show age, period, and cohort patterns - is retainedin the domain of compositions. The optimal choice among the four proposed techniquesdepends primarily on the number of groups making up the composition and whether ornot the plot should be readable by people with impaired colour vision. Contribution: We introduce techniques for visualizing compositional data on a period-age grid to thefield of demography and demonstrate the usefulness of the techniques by performingan exploratory analysis of age-specific French cause-of-death patterns across the 20thcentury. We identify strengths and weaknesses of the four proposed techniques. We contribute a technique to construct the ternary-balance colour scheme from within a per-ceptually uniform colour space. Comments: A full-colour representation is key to understanding the paper. Therefore, we recommend that you read it on screen or print a colour version.