What should be analysed?

• Density plot, histogram, violin plots

  • Mean value or typical value
  • Symmetry
  • Variation
  • Whether reminds some distribution
  • Heavy/Light tailed
  • One ore more modes
  • Skewness

What should be analysed?

• Box plot

  • Median
  • Variation
  • Outliers
  • Symmetry
  • Quantiles

Example: Visualizing miles per gallon depending on transmission type

• Y: dependent variable, X: independent variable
• Smoother is a good idea to have

Analysis:

• Shape (data=true+error, true=linear, quadratic, cubic, exponential, .., empirical)
  • How to find the right model?
    • Fitting the data (regression)
    • Analysis of residuals or model selection methods
• Strength (how close observations to a hypothized model)
  • If linear, Correlation r or coefficient of determination R2

Analysis:

• Direction (if monotonic, decreasing or increasing; if not monotonic, which parts increasing, which decreasing)
• Density (dense areas, sparse areas)
• Outliers
• Clusters

Example: Visualizing weight and rear axle ratio

• More variables can be mapped
  • Mark shape
  • Mark size
  • Mark color
  • Mark orientation
  • Juxtaposed displays or superimposed displays
• If juxtaposed displays used, we get
  scatterplot matrix

• Remember: interpolated data used
• Analysis:
  • Peaks and draughts
  • Trends
  • Additivity
  • Always check the underlying data after

• Geographical coordinates are involved
• Used in many applications
  • Climate modeling/analysis
  • Economic/social data analysis
  • Transaction data
  • …

• Point phenomena ( ex: building location, city location)
• Line phenomena (paths, roads)
• Area phenomena (counties)
• Surface phenomenon (mountains)

• Symbol/dot maps (nominal/ordinal point data)

• Land use maps/Choropleth maps (nominal/ordinal area data)

• Line diagrams (nominal/ordinal line data)

• Isoline maps (ordinal surface data)

• Surface maps (ordinal volume data)

• Note: Different maps can be used for the same data

  • Choropleth map / Dot map
  • Density surface /dot map

• Map coordinates:

  • longitude \(\lambda=[-180,180]\), negative=west
  • lattitude \(\phi=[-90,90]\), negative= south

• Challenge: \([\lambda, \phi] \rightarrow [x,y]\)

• Different map projections

  • Conformal projection: retains angles (shapes) but not area
  • Equal area: retains areas but not angles (shapes)
  • …

• Cylindrical projection, plane projection and cone projection
• Cylindrical projection used by Google, standard now

• Conformal projection: far northern/far southern areas inflated
• Defined by \(x=\lambda, y=\phi\)

• Albers Equal-area projection
  • Preserves areas
  • Shapes or distances are not correct

• Data= Lattitude, Longitude+ Other variables
• Latt, Long->Coord, Other variables–>Visual aesthetics
  • Amount is limited! (perception problems)
• Another approach: multiple parameters on multiple maps

• Analysis:
  • Density in geogr areas and between geogr areas
  • Spatial pattern of density (north, south)
  • Clusters, outliers
• Problems:
  • Overplotting in highly populated ares
  • If several observations have the same coordinate
  • Size aesthetics used–> perception problem
    • Perceived size depends on local neighborhood (Ebbinghaus illusion)
  • Color used: color perception problems

• Problems:
  • Absolute vs relative mapping (proportional to population)

• Observation: set of (Latt, Long) pairs+ other variables
• Often: start, end point

• Same as in network analysis plus
• geographical relationships between links and their density (size)
  • Where dense links located?
  • How links are directed?
• Problems:
  • Overplotting
  • If line length analysed -> length perception problem
  • If width analysed -> volume perception problem
  • Colors analysed ->color perception problem

• Overplotting - possible solution:
  • Using curved lines, minimize edge crossing

• Data: Name/Coordinates of geographic area+ other variables
• Choropleth maps: variables=color or shaded region on map

• Analysis:
  • Find clusters of regions that are similar
  • Find unusual regions (compared to neighbor regions)
  • Find patterns on the map
• Problems affecting perception:
  • Color/grayscale mapping
  • Choice of regions (county, state,…)
  • Larger region with the same color looks dominating
  • Patterns in small/densely populated areas hard to see

• Isarithmic maps: show areas of phenomenon on the map (density)
  • Contour map
  • Topographic map

• Plenty of commercial/Noncommercial software
  • ArcGIS, Google, Yahoo, Microsoft map API
• Plotly
  • plot_geo()
  • Using MapBox
• To use Mapbox:
  • Register with your email, find your token
  • Run in R Sys.setenv('MAPBOX_TOKEN' = 'your_mapbox_token_here')
• Ggplot2
  • geom_sf()
  • ggmap

• A few countries available through plotly
• Downloading map of a country:
  • Finding a country map http://gadm.org/
  • Decide what level of detalization is needed (region, county,…)
  • Download GeoGSON file, unzip if needed.
  • Read the JSON file into R
  • Use with ggplot()+geom_sf()
  • Use with Plotly: plot_geo()+add_trace(type=“choropleth”/ “scattergeo”)
  • Use with MapBox: plot_mapbox()+add_trace(type=“choroplethmapbox”/ “scattermapbox”)

• Given adresses/city/county-> coordinates?
• Go to http://www.gpsvisualizer.com/geocoder/
• Create MapQuest Open Key
• Paste locations in separate rows

• Chapter 6
• Plotly book, ch 2.2, 2.4 and 2.5