• Location: where things happen matters!
• Dependence is the rule: spatial interaction (contagion), spatial externalities (spillovers)
• scale matters: local vs. global — individual vs. total

The outcome changes when the locations of the objects under study changes. CONTEXT MATTERS!

• Descriptive — A question: “What, Where?”
• Inferential statistics — A hypothesis: “How, Why?”

• Descriptive — A question: “What, Where?”
• Inferential statistics — A hypothesis: “How, Why?”

• It tells us something more about what we’re studying. Transforming data into information!

• To incorporate spatial effects into models to avoid specification problems and to ensure satisfaction of statistical assumptions.

  • Spatial dependency may violate regression assumptions. Units of analysis might not be independent

  • If spatial effects are present, and you don’t account for them, your model is not accurate.

  • Make decisions with a higher level of confidence

• Inferential statistics: start with a null hypothesis
• Null hypothesis (H0): complete spatial randomness/ spatial independence
  • Any event has an equal probability of occurring at any position in the region
  • Position of any event is independent of the position of any other

• What is spatial association: Spatial objects tend to relate with one another
• The first law of Geography (Tobler): Everything is related to everything else, but near things are more related than distant things
  • But how related and why?
  • How near is “near”?

• Spatial heterogeneity (clustering): Non-uniform distribution of observations over space: space is not homogeneous (spatial regimes/spatial structure)
  • Apparent Contagion (reactive)
  • First order spatial effects
• Spatial Dependence/Autocorrelation: similar (or dissimilar) values in space tend to cluster together.
  • Sorting mechanism (Underlying socio-economic, environmental process has led to clustered distribution of variable values )
  • True Contagion?? (interaction): clusters of similar values
  • Second order spatial effects

• Analyzing Patterns: These tools evaluate if features, or the values associated with features, form a clustered, dispersed, or random spatial pattern.
• Mapping Clusters: These tools may be used to identify statistically significant hot spots, cold spots, or spatial outliers. There are also tools to identify or group features with similar characteristics.
• Measuring Geographic Distributions: These tools address questions such as Where’s the center? What’s the shape and orientation? How dispersed are the features?
• Modeling Spatial Relationships: These tools model data relationships using regression analyses or construct spatial weights matrices.
• Utilities: These utility tools perform a variety of miscellaneous functions: computing areas, assessing minimum distances, exporting variables and geometry, converting spatial weights files, and collecting coincident points.

• Geographical Weighted Regression (GWR)
• Geographical Temporal Weighted Regression (GTWR)

• Geographical Weighted Regression (GWR)
• Geographical Temporal Weighted Regression (GTWR)

Ordinary Least Squares corrected for spatial autocorrelation

(A). classic linear model

(B). spatial error model

(C). spatial lag model

(D). spatial Durbin model.

Spatial Statistics Resources

the Center for Spatial Data Science (CSDS)

GeoDa

Luc Anselin

CRP 4680 Introduction to Urban Data Science: Data, Interpretation, and Presentation