Beat Hulliger

The Quintile Share Ratio in location analysis

The inequality measure “Quintile Share Ratio” (QSR or sometimes S80/S20) is the primary income inequality measure in the European Union’s set of indicators on social cohesion. An important reason for its adoption as a leading indicator is its simplicity. The Quintile Share Ratio is “The ratio of total income received by the 20% of the population with the highest income (top quintile) to that received by the 20% of the population with the lowest income (lowest quintile)”. The QSR concept is used in this paper in the context of obnoxious facility location where the inequality is in distances to the obnoxious facility. The single facility location problem minimizing the QSR is investigated. The problem is investigated for continuous uniform demand in an area such as a disk, a rectangle, and a line; when demand is generated at a finite set of demand points; and when the facility can be located anywhere on a network. Optimal solution algorithms are devised for demand originating at a finite set of demand points and at nodes of the network. Computational experiments demonstrate the effectiveness of the algorithms.

Combining geographical information and traditional plots: the checkerplot

The checkerplot is a new type of graphical display that combines geographical information and statistical plots. Hereby, the traditional plots like barplots or polygon lines are visualized in geographical order on a grid. The checkerplots can be seen as a mixture between thematic maps and the grid representation in trellis plots. In a checkerplot, any complex statistical graphics that are produced for geographical areas are placed in a grid. An interpretable checkerplot requires an arrangement of areas on the grid that reflects the underlying geography. A loss function is proposed that represents the distortion of the underlying geography needed in order to place the areas onto a grid. It is demonstrated that the minimization of the loss function does indeed produce interpretable checkerplots. Moreover, the optimization problem can be formulated as a linear programming problem that can be solved using standard linear programming solvers. The proposed checkerplot is applied to US health insurance data to analyze the development of the coverage rate in the health system per state with respect to the different health care programs. Moreover, an example related to the EU-member states is also given. Additional information like the national flags of countries are placed in each grid to allow better visibility and recognition of the countries. The checkerplot is implemented in the R-package sparkTable (Kowarik, Meindl, and Templ, 2012. sparkTable: sparklines and graphical tables for tex and html [online]. R package version 0.9.3 [Accessed 7 February 2012]) and can be freely downloaded from the CRAN repository. It is implemented in a flexible manner and not restricted to the examples given in this contribution.