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Class 21

Spatial Regressions

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AGENDA

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Today’s Class …

  • Spatial Regressions

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During Class …

  • Spatial Regression Activity

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Next Class …

  • Spatial Analysis

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Geography’s Quantitative Revolution

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  • “The Problem of Spatial Autocorrelation” (1969). Andrew Cliff and Keith Ord

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  • Realization that classical statistics can be inappropriate for modeling geographical phenomena (Tobler’s first law of geography)

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  • Increasing need for a statistic that tests for spatial pattern, or spatial autocorrelation

Type 1 Error 👎 👎 👎

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Spatial Autocorrelation

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  • The degree of similarity between objects that are located near each other

�Global Moran’s I- Measures the magnitude of spatial autocorrelation. Returns a single result (I). In addition, provides a p-value (the probability associated with I). 

    • Ranges from -1 to 1 (-1 is perfectly dispersed, 0 is random, 1 is perfectly clustered)
    • Compared I of observed data to expected I (expected under complete spatial randomness) 

�Local Moran’s I- Iterates through each observation and provides a measure of autocorrelation and p-value

    • Results can be mapped

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What’s the Problem?

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  • One of the regression assumptions is independence of observations.
  • If observations are not independent, we get inaccurate estimates of the coefficients
  • This leads to biased error terms (residuals AKA what is not explained by the model) because the error terms contain spatial dependencies
  • This is a big problem!

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Spatial Autoregressive Models

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  • Spatial Error Model- Clustering is due to spatial processes inherent to the independent variables that are both measured and omitted from the model. 

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  • Spatial Lag Model- Represents a diffusive process. The value of a variable is influenced by the value in another neighboring location 

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  • Deciding which one:
    • Statistical testing
    • Theoretical considerations

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Basic Steps

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  1. Run a traditional regression
  2. Determine if the residuals of that regression show spatial dependency (Moran’s I)
  3. If there is no dependency, you’re all good!
  4. If there is dependency, think theoretically- what model type do you think might be most appropriate?
  5. Run models
  6. Compare fit to original linear regression

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Using SAM

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Source: https://www-sciencedirect-com.libproxy.lib.unc.edu/topics/computer-science/spatial-autocorrelation

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