Summary about all contents for the exam, including Spatial Analysis, Geodata models, Geodatabases, Python Programming, Spatio-Temporal Modelling, Geodata Dissemination
GIMA Module 5 Summary all themes
1.Spatial Analysis
L: Introduction to (Spatial) Regression Models
Spatial analysis aims to:
- Evaluate how entities are spatially distributed
- Determine the underlying spatial processes
- Analyse the relationships between patterns
The focus here is on spatial entities represented as polygons (e.g. municipalities) or points (e.g
houses) » qualitative and quantitative attributes are attached.
Spatial Autocorrelation (SAC)
Grounds on the First Law of Geography: All things are related, but nearby things are more related
than distant things.
➢ Values observed at one location depend on the values of neighbouring observations.
Positive SAC
Similar values are spatially close-by
Negative SAC
Dissimilar values are spatially close-by
No SAC
Spatially random distribution (geography does not matter)
Spatial Heterogeneity (SH)
Characteristics of a population / sample depends on the absolute location
Patterns vary over space, there are no ‘average places’.
Why does space matter?
➢ Why is it important to know how a pattern is distributed?
- The data is not independent
- SAC has serious consequences for non-spatial statistical analysis » it might result in wrong
conclusions.
Exploratory spatial data analysis
Aims to discover spatial patterns
3 kinds of approaches:
Mapping
- E.g. choropleths
Global methods
Local methods
Global statistics
The spatial characteristics of a pattern are summarized globally
➢ One single number represents the pattern » it approximates an ‘average’ value.
, ➢ Spatial variations cannot be detected
Methods:
- Join Count statistic: for nominal data
- Moran`s I: interval / ratio data
- Geary`s C: interval / ratio data
- Autoregressive models
Step 1: definition of the spatial system
Contiguity (nabijheid) :
Rooks contiguity (touches only the 4 line-sharing polygons) & Queens contiguity (touches all point-
sharing polygons)
K-nearest neighbours:
K closest entities are defined as neighbours, this avoids island effects.
Threshold distance:
Entities within a particular distance (circle area) are defined as neighbours.
➢ E.g. points within 100 meters are defined as neighbours.
Interaction:
Spatial closeness results in similarity. I.e. closer entities have greater influence than more distant
ones.
For example: 1 = full interaction; 0 = no interaction.
Common functions are:
- Inverse distance weighting: wij = 1 / dij
- Squared distance weighting: wij = 1 / dij2
o Relative influence drops off more rapidly.
The W matrix (n x n)
Row standardisation:
Spatial weights are rarely used in their binary form, W is often standardised.
In row standardisation, each weight is divided by the sum of its row. So each row sums up to 1.
This allows comparison between parameters.
Step 2: select a statistic
Moran’s I
Moran’s I tests for global spatial autocorrelation:
“Are (dis)similar values in close proximity to each other or are they randomly distributed?”
The range is from + 1 (Positive SAC) to - 1 (Negative SAC). When around 0: no correlation (spatial
randomness).
Permutation approach (to check significance):
Calculate for a high number of maps (e.g. 999 runs) the Moran’s I.
If the observed Moran’s I lies in a tail of the distribution, then this is evidence for a significant value.
Local statistics
When using the global SAC, this provides evidence concerning spatial associations, but no
statements about the ‘where’ are possible.
Local statistics have the following advantages:
- Detection of clusters
, - Output of many parameters
- Visualisation capabilities
- Explore heterogeneity.
The following methods can be used:
- Local Moran’s I
- G* - statistic
- GWR
Local Moran’s I
This is a local disaggregation of the global coefficient.
It determines attribute similarity for each unit in comparison to its neighbourhood.
This enhances the detection of:
- Hot spots: High values surrounded by high values
- Cold spots: Low values surrounded by low values
- Outliers: High values surrounded by low values
Low values surrounded by high values
Moran scatterplot
The Moran scatterplot describes the linear relation of attribute values to its neighbours.
Covariance and correlation
Covariance
Measures the association between 2 continuous variables
Pearson product-moment correlation coefficient
Standardised measure of the linear association between 2 variables.
Regression
Regression informs about the form and the nature of a relationship
➢ E.g. how is distance to the core city related to housing prices?
Simple regression:
1 response variable (dependent, metric scale), 1 independent variable (predictor)
➢ E.g. house price = f(floor area)
, Intercept = point at which the line crosses the vertical axis.
Ordinary least squares (OLS) approach
This is a statistical approach to determine the ‘best’ fitting line in a scatterplot.
- Minimizes the squared residuals.
o The black line ^ describes the data as close as possible.
In the equation (see above):
ß’s give insights into the nature of the association
ß0 gives the estimated value of y when x = 0
ß1 says how y varies when x is increased by 1 unit.
Model validation:
After estimating a regression, the following needs to be done:
- Validation of the model quality
- Statistical significance of the estimated parameters
- Fundamental model assumptions
Essential are:
- (adjusted) coefficient of determination (R2)
- T-statistic
- F-statistic
- Akaike Information Criterion (AIC)
- Moran’s I of the regression residuals.
Coefficient of determination (R2)
R2 tests how well a models explains the data.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller nielsvenema. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.03. You're not tied to anything after your purchase.
