Multivariate Mapping

Multivariate mapping is the visual exploration of multiple attributes using a map or data reduction technique. More than one attribute can be visually explored and symbolized using numerous statistical classification systems or data reduction techniques. Complex data relationships can be visually displayed using graphical symbols. Color encodings are used to represent spatial relationships in a given data set in a logical sequence and interpretable format. To successfully communicate these complex spatial relationships, serious attention must be paid to human cognitive factors and perception. In practice, most small-scale data sets are usually displayed using graduated colors, graduated symbols, proportional symbols, dot density, bar charts, and stacked charts, among others. More recently, large-scale data sets have been represented using more complex data reduction techniques.

A set of visual variables (e.g., texture, orientation, color, size, shape, arrangement, and pattern) is available to facilitate the display and cartographic representation (symbol encoding) of multiple attributes. However, thoughtfulness in terms of map design, organization, and presentation of final results is required; symbols must be logically organized in a sequence that provides visual clarity so that the information can be easily decoded; and more important, the information must be successfully displayed and effectively communicated to the intended audience. Choosing colors can be quite challenging, but recent work by Cynthia Brewer has resulted in a very helpful guide to choosing a color scheme.

Examples from a geovisualization course are provided to illustrate the concept of multivariate mapping. In this course, students explored two data sets: (1) the first set depicted the relationship between murder rates and families in poverty in selected cities of the United States and (2) the second set depicted housing ownership covering a period from 1900 to 2000. The examples demonstrate the analysis of the covariation among variables within and between the two data sets with the intent of simplifying and visually displaying selected variables.

The use of multivariate mapping allows uncovering of the underlying relationships in data, developing study hypotheses, and the description of complex spatial relationships. From the analyses of the two data sets, three study hypotheses were defined:

• 1.
  There is a spatial association between increased murder rates and the percentage of families living in poverty in selected cities in the United States.
• 2.
  Murder rates are higher in cities located in the East Coast than in cities located elsewhere in the United States.
• 3.
  Housing ownership is closely associated with economic expansion and prosperity.

In Figure 1, several plots are presented to illustrate a few variables that may influence murder rates in the United States. The upper panel in Figure 1 has a map, a histogram, and a table. The histogram is used to represent and explore the distribution of the young adult population at a county level. The table summarizes high murder rates, while the choropleth map is overlaid with a proportional symbol map to evaluate whether there is a visual association between murder rates and potentially related variables. A subset of young adults (ages 18–29) is explored together with the murder rates. The six divergent classes are symbolized using a ColorBrewer color scheme, with areas shown in red having the highest numbers and areas in blue having the lowest. In this multivariate map, graduated colors and proportional symbols have been used to represent murder in relation to young adults. From this map, we can infer that the West and Midwest have a lower number of young adults. The red area appears to be more concentrated in the central/eastern side of the United States. There is no apparent visual association between cities with the highest murder rates and cities with large populations of young adults. The lower panel in Figure 1 has a scatter plot, and a dot density map is linked, with proportional symbols representing different murder rates. This plot shows only a very small relation of young adults and population density to increased murder rates, and the highest murder rates appear in areas of high population density. The plot uncovers the fact that in some cities, such as those located in [Page 1964][Page 1965]Mississippi and Alabama, high murder rates are not necessarily associated with high population density. This demonstrates that association does not imply causality.

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