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{{Short description|Thematic map visualizing multiple variables}}
[[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 different sets of [[Map symbol
The typical objective of a multivariate map is to visualize any statistical or geographic [[Correlation and dependence|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 [[Cognitive overload]] when the symbols and patterns are too complex to easily understand.<ref name="slocum2009">T. Slocum, R. McMaster, F. Kessler, H. Howard (2009). Thematic Cartography and Geovisualization, Third Edn. Pearson Prentice Hall: Upper Saddle River, NJ.</ref>{{rp|331}}
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==History==
[[File:Minard-carte-viande-1858.png |thumb|right|300px| 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 [[
[[Charles Joseph Minard]] became a master at creating visualizations that combined multiple variables during the 1850s and 1860s, often mixing [[Choropleth map
Multivariate thematic maps found a resurgence starting in the middle of the 20th Century, coinciding with the [[Quantitative revolution
Starting in the 1980s, computer software, including the [[Geographic information system]] (GIS) facilitated the design and production of multivariate maps.<ref>Dunn R., (1989). [https://www.jstor.org/stable/2685372 A dynamic approach to two-variable color mapping]. ''The American Statistician'', Vol. 43, No. 4, pp. 245–252</ref> In fact, a tool for automatically generating bivariate choropleth maps was introduced in [[Esri]]'s ArcGIS Pro in 2020.
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* A ''multi-layered thematic map'' portrays the variables as separate map layers, using different [[thematic map]] techniques. An example would be showing one variable as a [[choropleth map]], with another variable shown as [[Proportional symbol map|proportional symbols]] on top of the choropleth.
* A ''correlated symbol map'' represents two or more variables in the same thematic map layer, using the same [[visual variable]], designed in such a way as to show the relative combination of the two variables.
** A ''bivariate [[choropleth map]]'' is the most common type of correlated symbol. Contrasting but not
** A ''multivariate [[Dot distribution map
* A ''multivariate symbol map'' represents two or more variables in the same thematic map layer, using distinct [[
** A ''[[cartogram]]'' distorts the size and shape of a set of districts according to a variable, but does not dictate the symbol used to draw each district. Thus it is common to symbolize them as a [[choropleth map]].
** A ''chart map'' represents each geographic feature with a [[Chart
** ''[[Chernoff face
* A ''[[small multiple]]'' is a series of small maps, arranged in a grid or array, each of which shows a different (but possibly related) variable over the same space.<ref name="Tufte-EI">{{cite book |last1=Tufte |first1=Edward |title=Envisioning Information |date=1990 |publisher=Graphics Press |isbn=978-0961392116 |page=[https://archive.org/details/envisioninginfor0000tuft/page/67 67] |url=https://archive.org/details/envisioninginfor0000tuft/page/67 }}</ref> It has been argued that this is not technically a multivariate map because it is a set of separate maps,<ref name="gistbok" /> but it is included here because it is intended to accomplish the same purpose.
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Multivariate thematic maps can be a very effective tool for discovering intricate geographic patterns in complex data.<ref name="gistbok" /> If executed well, related patterns between variables can be recognized easier in a multivariate map than by comparing separate thematic maps.
The technique works best when the variables happen to have a clear geographic pattern, such as a high degree of [[spatial autocorrelation]], so that there are large regions of similar appearance with gradual changes between them, or a generally strong correlation between the two variables. If there is no clear pattern, the map can become an overwhelming mix of random symbols.
A second problem occurs when the symbols do not harmonize well. In keeping with [[Gestalt psychology]], a multivariate map will work best when map readers can isolate patterns in each variable independently, as well as comparing them to each other. This occurs when the [[
A third issue arises when a map, or even a single symbol, is overloaded with too many variables that cannot be efficiently interpreted.<ref name="torguson">{{cite book |last1=Dent |first1=Borden D. |last2=Torguson |first2=Jeffrey S. |last3=Hodler |first3=Thomas W. |title=Cartography: Thematic Map Design |date=2009 |publisher=McGraw-Hill |isbn=978-0-07-294382-5 |page=147}}</ref> Chernoff faces have often been criticized for this effect.
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* [[Domain coloring]]
* [[Four color theorem]]
* [[Multivariate function]]
== References ==
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=== Other Literature ===
*Jeong W. and Gluck M., (2002). [[Multimodal interaction|Multimodal]] bivariate thematic maps with auditory and haptic display. Proceedings of the 2002 International Conference on Auditory Display, Kyoto, Japan, July
*Leonowicz, A (2006). Two-variable choropleth maps as a useful tool for visualization of geographical relationship. Geografija (42) pp.
*Liu L. and Du C., (1999). Environmental System Research Institute (ESRI), online library.
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