Multivariate map: Difference between revisions

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[[File:Black Hispanic Bivariate Map.png|thumb|400px|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 [[Variable (mathematics)|variables]] on a single [[map]] by combining two different sets of graphic[[Map symbol | symbols]].<ref orname="slocum2009">T. Slocum, colorsR. BivariateMcMaster, mappingF. Kessler, H. Howard (2009). Thematic Cartography and Geovisualization, Third Edn. Pearson Prentice Hall: Upper Saddle River, NJ.</ref>{{rp|331}} Each of the variables is anrepresented importantusing techniquea instandard [[cartographythematic map]]. Ittechnique, issuch aas variation[[Choropleth ofmap simple| choropleth]], [[choroplethcartogram]], or [[Proportional symbol map | proportional symbols]]. thatThey portraysmay twobe the same type or different types, and they may be on separate phenomenalayers of the map, or they may be combined into a single multivariate simultaneouslysymbol. The maintypical objective is to accuratelyvisualize andany graphicallystatistical illustrateor thegeographic [[Correlation and dependence|relationship]] between two spatially distributedthe variables. It has potential to reveal relationships between variables more effectively than a side-by-side comparison of the corresponding univariate maps.

==History==

[[File:Minard-carte-viande-1858.png | 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 meat, combined with pie charts showing the composition 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 map | 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]].<ref name="robinson1955">{{cite journal |last1=Robinson |first1=Arthur H. |title=The 1837 Maps of Henry Drury Harness |journal=The Geographical Journal |date=Dec 1955 |volume=121 |issue=4 |pages=440-450 |url=https://www.jstor.org/stable/1791753}}</ref><ref name="harness1837">{{cite book |last1=Griffith |first1=Richard John |last2=Harness |first2=Henry Drury |title=Atlas to Accompany 2nd Report of the Railway Commissioners |date=1838 |___location=Ireland |url=http://digital.ucd.ie/view/ivrla:45724}}</ref>

[[Charles Joseph Minard]] became a master at creating visualizations that combined multiple variables, often mixing [[Choropleth map | choropleth]], [[Flow map|flow lines]], [[Proportional symbol map |proportional symbols]], and [[Chart|statistical charts]] to tell complex stories visually.<ref name="tufte2006">{{cite book |last1=Tufte |first1=Edward |title=Beautiful Evidence |date=2006 |publisher=Graphics Press}}</ref>

The first modern bivariate choropleth maps were published by the U.S. Census Bureau in the 1970s.<ref>{{cite journal |last1=Meyer |first1=Morton A. |last2=Broome |first2=Frederick R. |last3=Schweitzer |first3=Richard H. Jr. |title=Color Statistical Mapping by the U.S. Bureau of the Census |journal=The American Cartographer |date=1975 |volume=2 |issue=2 |pages=101-117 |doi=10.1559/152304075784313250}}</ref> 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.<ref name="Olson1981">{{cite journal |last1=Olson |first1=Judy M. |title=Spectrally encoded two-variable maps |journal=Annals of the Association of American Geographers |date=1981 |volume=71 |issue=2 |pages=259-276}}</ref>.

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.