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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'''
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}}
==History==
[[File:Minard-carte-viande-1858.png |thumb|
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.
== Advantages and criticisms ==
[[File:2016 US Presidential Election Pie Charts.png|thumb|right|300px|A multivariate symbol map of the 2016 U.S. presidential election, using a combination proportional and chart symbol]]
[[File:Dot map black hispanic.png|thumb|left|A bivariate dot density map showing the distribution of the African American (blue) and Latino (red) populations in the contiguous United States in 2010.]]
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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