Spatial statistics using polygon data

We will work with polygons completely covering the analyzed area (artificial polygons representing administrative units) and will assess clustering of polygons with high or low values – spatial autocorrelation. We will try methods introduced during the lectures using data from elections and census and then you will work with an attribute by yourself. We will use the software GeoDa and also ArcMap. We can use also the software CrimeStat that contains the same methods.

Detail documentation of Spatial Autocorrelation and Spatial Regression in GeoDa is here.

• global spatial autocorrelation,
• local spatial autocorrelation,
• spatial regression (read chapters 22-25).

Firstly we will consider a spatial neighbourhood:

1. in GeoDa, you can select from three different ways how to define a neighbourhood (weight) in a binary way: topological (queen and rook), threshold distance and k nearest neighbours. Create an example of each for you data and district.
2. the created weights can be analyzed using connectivity histogram. Compare created weights and describe results. Try to consider differences and estimate, how will the differences influence results.
3. Conclude positives and negatives of particular neighbourhoods.

Global characteristics of spatial autocorrelation

1. in GeoDa, Moran’s I is the only statistic to assess the global autocorrelation;
2. calculate Moran’s I for all three types of weight;
3. compare results and check if the results are the same as your previous conclusion;
4. using the method Monte Carlo consider statistical significance of results;
5. look at the Moran’s scatterplots and describe results;
6. create weights using additional two threshold distances and create a correlogram analyzing a relationship between threshold distance and Moran’s I;
7. try the Getis-Ord General G and Geary’s C that are implemented in ArcMap. Compare the results with Moran’s I.

Local characteristics of spatial autocorrelation (LISA)

1. Local Moran’s I as well as Gi and Gi* are implemented in GeoDa ;
2. calculate local spatial autocorrelation using local Moran’s I for the spatial weight with the highest global Moran’s I;
3. using the Monte Carlo method test statistical significance of results;
4. create a map with clusters (Cluster Map), look at significance map and describe results- an existence of hot and cold spots;
5. calculate Gi* for the same data, describe results and compare them with Moran’s I.

Spatial regression models

We will work with the same data about elections extended about data from census. The regression model will explain a variability of dependent variable – relative number of votes for a political party. In GeoDa, linear regression (OLS method) and two spatial regression models are implemented (spatial lag model and spatial error model).

1. create contiguity spatial weight (queen)
2. create a model using linear regression similarly as during one of previous seminar
3. select created spatial weight to test spatial autocorrelation as a part of regression restults
4. interpret the results and modify the model according to your knowledge and using selected approach (backward, stepwise etc.)
5. intepret the results of the best models and consider the influence of spatial autocorrelation and select the best spatial regression model
6. apply the spatial regression model, modify it and compare them with results of previous linear regression model
7. show in a map residuals and consider their spatial autocorrelation

Geographic weighted regression

Metoda geografické vážené regrese je implementována v programu ArcMap a to v Toolboxu Spatial Statistics Tools/Modeling Spatial Relationships. V nastavení této funkce je opět možné definovat závislou a nezávislé proměnné a dále detailnější nastavení – typ volby dosahu – fixní nebo adaptivní a dále pak metodu stanovení délky dosahu, kdy jsou k dispozici tři varianty – dle Akaike kritéria, křížovou validací (automatická volba kroku) a nebo pevná vzdálenost (při volbě fixního dosahu) nebo pevný počet sousedů (při volbě adaptivního dosahu).

Individual task 4

You will follow the bullets below using election (2017) and census (2011) data on the level of districts.

Deadline: 31. 12. 2017

Cvičení je vytvořeno v rámci projektu Inovace bakalářských a magisterských studijních oborů na Hornicko-geologické fakultě VŠB-TUO pod číslem CZ.1.07/2.2.00/28.0308. Tento projekt je realizován za spoluúčasti EU.