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Multivariate map

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Bivariate choropleth map comparing the Black (blue) and Hispanic (red) populations in the United States, 2010 census; shades of purple show significant proportions of both groups.

A bivariate map (or multivariate map) is a type of thematic map that displays two or more variables on a single map by combining two different sets of symbols.[1]: 331  Each of the variables is represented using a standard thematic map technique, such as choropleth, cartogram, or proportional symbols. They may be the same type or different types, and they may be on separate layers of the map, or they may be combined into a single multivariate symbol.

The typical objective of a multivariate map is to visualize any statistical or geographic relationship between the variables. It has potential to reveal relationships between variables more effectively than a side-by-side comparison of the corresponding univariate maps, but also has the danger of Information overload when the symbols and patterns are too complex to easily understand.

History

An 1858 multivariate map by Charles Joseph Minard, using a nominal choropleth to represent departments that supplied meat to be consumed in Paris, proportional circles to represent significant volumes of that meat, combined with pie charts dividing it into relative proportions of beef (black), veal (red), and mutton (green).

The first multivariate maps appeared in the early Industrial era (1830-1860), at the same time that thematic maps in general were starting to appear. An 1838 booklet of maps produced by Henry Drury Harness for a report on Irish railroads included one that simultaneously showed city populations as Proportional symbols and railroad traffic volume as a Flow map.[2][3]

Charles Joseph Minard became a master at creating visualizations that combined multiple variables, often mixing choropleth, flow lines, proportional symbols, and statistical charts to tell complex stories visually.[4]

The first modern bivariate choropleth maps were published by the U.S. Census Bureau in the 1970s.[5] Their often complex patterns of multiple colors has drawn acclaim and criticism ever since, but has also led to research to discover effective design techniques.[6].

In recent years, computer software, including the Geographic information system (GIS), has facilitated the design and production of multivariate maps. In fact, a tool for automatically generating bivariate choropleth maps was introduced in Esri's ArcGIS Pro in 2020.

Methods

Bivariate mapping is a comparatively recent graphical method. A bivariate choropleth map uses color to solve a problem of representation in four dimensions; two spatial dimensions — longitude and latitude — and two statistical variables. Take the example of mapping population density and average daily maximum temperature simultaneously. Population could be given a colour scale of black to green, and temperature from blue to red. Then an area with low population and low temperature would be dark blue, high population and low temperature would be cyan, high population and high temperature would be yellow, while low population and high temperature would be dark red. The eye can quickly see potential relationships between these variables.

Example of a bivariate thematic map, displaying minority proportion as a choropleth, and family size as a proportional symbol

Data classification and graphic representation of the classified data are two important processes involved in constructing a bivariate map. The number of classes should be possible to deal with by the reader. A rectangular legend box is divided into smaller boxes where each box represents a unique relationship of the variables.

In general, bivariate maps are one of the alternatives to the simple univariate choropleth maps, although they are sometimes extremely difficult to understand the distribution of a single variable. Because conventional bivariate maps use two arbitrarily assigned color schemes and generate random color combinations for overlapping sections and users have to refer to the arbitrary legend all the time. Therefore, a very prominent and clear legend is needed so that both the distribution of single variable and the relationship between the two variables could be shown on the bivariate map.

See also

References

  • Dunn R., (1989). A dynamic approach to two-variable color mapping. The American Statistician, Vol. 43, No. 4, pp. 245–252.
  • Jeong W. and Gluck M., (2002). Multimodal bivariate thematic maps with auditory and haptic display. Proceedings of the 2002 International Conference on Auditory Display, Kyoto, Japan, July 2-5.
  • Leonowicz, A (2006). Two-variable choropleth maps as a useful tool for visualization of geographical relationship. Geografija (42) pp. 33–37.
  • Liu L. and Du C., (1999). Environmental System Research Institute (ESRI), online library.
  • Olson J. (1981). Spectrally encoded two-variable maps. Annals of the Association of American Geographers. 71 (2): 259-276.
  • Trumbo B. E. (1981). A theory of coloring bivariate statistical maps. The American Statistician, Vol. 35, No. 4, pp. 220–226.
  1. ^ T. Slocum, R. McMaster, F. Kessler, H. Howard (2009). Thematic Cartography and Geovisualization, Third Edn. Pearson Prentice Hall: Upper Saddle River, NJ.
  2. ^ Robinson, Arthur H. (Dec 1955). "The 1837 Maps of Henry Drury Harness". The Geographical Journal. 121 (4): 440–450.
  3. ^ Griffith, Richard John; Harness, Henry Drury (1838). Atlas to Accompany 2nd Report of the Railway Commissioners. Ireland.
  4. ^ Tufte, Edward (2006). Beautiful Evidence. Graphics Press.
  5. ^ Meyer, Morton A.; Broome, Frederick R.; Schweitzer, Richard H. Jr. (1975). "Color Statistical Mapping by the U.S. Bureau of the Census". The American Cartographer. 2 (2): 101–117. doi:10.1559/152304075784313250.
  6. ^ Olson, Judy M. (1981). "Spectrally encoded two-variable maps". Annals of the Association of American Geographers. 71 (2): 259–276.
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