8. Maps

8.1. Map

1. Definition: a map is a collection of spatially defined objects (Mark Monmonier)

2. Beyond mapping

   • Map as analysis vs Map as presentation

     • Geo-visualization

     • Geospatial visual analytics

   • Exploratory spatial data analysis (ESDA) - Luc Anselin

     • Spatial regimes: Spatial regimes are a form of spatial heterogeneity, which implies structural differences across space.

     • When a variable is characterized by distinct distributions (e.g., with a different mean or variance) for different geographic subregions, these subregions might point to the existence of spatial regimes.

8.1.1. Traditional Knowledge Discovery

1. Deductive approach

   • Hypothesis first, data later

2. Inductive approach

   • Data first, hypothesis later

3. Abductive approach

   • Pattern discovered along with hypothesis

   • Interaction between data exploration and human perception

8.2. Map Design Primer

8.2.1. How to Lie with Maps

1. Manipulate map design parameters

   • Scale, Symbols, Legends, Colors, Intervals

2. Choice of Projection

   • Larger areas seems more important

   • Conformal = Preserve angle

   • Equal area = Preserve area

   • Equal distant = Preserve distance

   • Azimuthal = preserve direction

3. Human Perception can be tricked

8.2.2. Choropleth Map

1. Visualizing a spatial distribution

   • Natural Breaks VS Quantile

   • Natural Breaks use clustering algorithm (minimum the heterogeneity within classes)

   • Natural Breaks have different number of observations per category

8.3. Continuous Statistical Maps

8.3.1. Percentile Map

1. Special form of Quantile Map - Percentiles

2. 6 categories instead of 100 categories

   • < 1%, 1-10%, 10-50%, 50-90%, 90-99%, >99%

3. Emphasis on Extremes - Away from median

4. Only works well for large data sets

   

8.3.2. Box map plot (Luc Anselin)

1. Box and whiskers plot

   • Identify shape of distribution and outliers

   • Focus on median

2. Inter quartile range (IQR)

   • Range from 25% to 75%

   • Fence = 75%/25% \(+/-\) 1.5 IQR or \(+/-\) 3 IQR

     • Outliers = outside the fence

   

8.3.3. Standard Deviation Map

1. Based on standardized data value

   • Mean = 0, standard deviation = 1

2. Intervals correspond to one standard deviation

3. Outliers are more than 2 standard deviations from the mean

   

8.4. Categorial Statistical Maps

8.4.1. Co-Location Map

1. Unique value map or Categorical map

   • For discrete categories

2. Map overlay

   • Map algebra

   • Matching categories between two or more maps

   

3. Multivariate categorical association

   1. Transfer box plot into categorical map (1-6)

   2. Find the overlap of the categories (rank)

   

8.4.2. Cartogram

1. Areal unit proportional to variable of interest

2. Avoid misleading effect of area

   

3. Use transformed shapes

   • Circular cartogram and Contiguous cartogram

   

8.4.3. Conditional Map

1. Special case of trellis/facet/conditional graphs

2. Micro-map matrix

   • Conditioning variables on axes

   • Matrix of mini maps for the variable of interest conditioned by values on the axes