Abstract
We introduce convex hulls as a data visualization and analytic tool for demography. Convex hulls are widely used in computer science, and have been applied in fields such as ecology, but are heretofore underutilized in population studies. We briefly discuss convex hulls, then we show how they may profitably be applied to demography. We do this through three examples, drawn from the relationship between child and adult mortality (5q0 and 45q15 in life table notation). The three examples are: (i) sex differences in mortality; (ii) period and cohort differences and (iii) outlier identification. Convex hulls can be useful in robust compilation of demographic databases. Moreover, the gap/lag framework for sex differences or period/cohort differences is more complex when mortality data are arrayed by two components as opposed to a unidimensional measure such as life expectancy. Our examples show how, in certain cases, convex hulls can identify patterns in demographic data more readily than other techniques. The potential applicability of convex hulls in population studies goes beyond mortality.
Highlights
We propose convex hulls as a technique of demographic analysis, illustrated by three examples
Throughout, we refer to cross-classification of child and adult mortality as the mortality relationship, and, as applicable, the mortality hull
As we show here without the formalism, this framework applies to sex differences
Summary
We propose convex hulls as a technique of demographic analysis, illustrated by three examples. The convex hull of a set of points is the region defined by a perimeter in which the line segment connecting any two points lies on or inside the perimeter. An informal heuristic is that if a set of points consists of pegs in a board, the convex hull is the shape of a rubber band stretched around the outermost pegs, such that all the pegs are enclosed by the band. The unique convex hull is illustrated as a white polygon (1C). Line segments connecting any two points in the data may be an edge of the convex hull, or interior, but cannot pass outside of it. Convex hulls exist in all dimensions: as a range (line segment) for unidimensional data, as polygons in R2 («2D»), as polyhedra in
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