Lecture 5 - Mapping and Modelling Geographic Data in R

Mapping and ModellingGeographic Data in R

Lecture 5

Spatial regression

Part 1, Intro to R Intro to statistics Intro to regression

Part 2, Mapping in R

GeographicalDataScience

Part 3, Spatial analysis in R

Vs

'Local'

'Global'

Geographically Weighted Statistics

Spatial smoothing

Geographically Weighted Statistics

Spatial interpolation

Geographically Weighted Statistics

Examiningspatially varyingrelationships ... which takes us to ...

Models and Explanation

COVID-19 rates in North EastEngland

Fit the model in R

Response (dependent) variable (Y)

Regression

Effect sizes (beta values)

Measures of statistical significance

Predictor (independent) variables (the Xs)

Model fit

Spatial patterns in the residuals

Not surprising

(but also not inevitable)

Spatial regression models

(examples of)

Spatial error model Spatially lagged y model

Spatial regression models

Spatial error model

Spatial regression models

Spatially lagged y model

Effect sizes (beta values)and now more complicated because of direct and indirect effects

Geographically Weighted regression

Another example of a geographically weighted statistic

The idea is a bit like this but instead going from point to point across the study region and adding geographical weighting

Geographically Weighted regression

These show how the regression estimated effect sizes vary from location to location across the study region There is a statistical test for this spatial variartion available

Not all the estimated effect sizes are necesserily statistically signifcant

Extension to standard GWR

Mixed GWR Multiscale GWR Geographicaly and temporally weighted regression Generalised GWR models

Anyquestions?