July 2018

Overview

Three Variations on Regression

  • Robust Regression
    • Minimising the effects of outliers
  • Geographically Weighted Regression
    • Allowing coefficients to change geographically
  • Poisson Regression
    • Working with counts as the \(y\)-variable

Robust Regression

Robust regression

Geographically Weighted Regression

Tobler’s first law of Geography

everything is related to everything else, but near things are more related than distant things. (Tobler, 1970)

Justification

“the full range of conditions anywhere on the Earth’s surface could in principle be found packed within any small area. There would be no regions of approximately homogeneous conditions to be described by giving attributes to area objects. Topographic surfaces would vary chaotically, with slopes that were everywhere infinite, and the contours of such surfaces would be infinitely dense and contorted. Spatial analysis, and indeed life itself, would be impossible.” (de Smith et al 2007, p44)

GWR

Coefficients change over the map:

Some coefficients flip…

So what we see here are the local variations in the degree to which changes in different variables are associated with changes in Median Income. The maps above are not simply maps of the predictor variable.

Poisson Regression

Basically A Different Distribution for \(y\)

  • Y is a count variable
    • Takes values \(0, 1, 2, \cdots\)
    • We model the log of the expected count value
    • Assume distribution is Poisson
  • Details in the notes.