- Overview of (some) statistical techniques that explicitly include
**space** - Focus on methods directed at Social Scientists (lattice data)
- Computer labs to demonstrate how to perform some of these analysis (scheduling
*"roughly"*split 50-50, but accomodating content)

*Pointing*more than*delving*deep*T**o**d**a**y*∈*A**l**l*but $All \notin Today$

- References
Interactive classes → Stop, interrupt and ask me!!!

... but could also be called spatial modelling:

- Point pattern analysis
- Spatial prediction (geostatistics, kriging...)
- Conditional models
- Bayesian estimation

Morning:

- Spatial data for social scientists
- Why spatial analysis?
- Spatial autocorrelation

After-noon:

- Spatial weights matrices
- The spatial lag operator
Exploratory Spatial Data Analysis (ESDA)

- Global
- Local

Spatial regression

- Motivation
- Specification
- Diagnostics
- Estimation
- Software implementation

Inserted between lecture time to be closer to the contents

**[I]**GIS: QGIS**[II]**Exploratory analysis: GeoDa**[III]**Spatial regression: GeoDaSpace**[IV]**Code: PySAL

- Observations that can be related to a location in (geographical) space
- Multiple formats:

[Ben Fry. *All Streets*]

- Popularization of locational technologies (e.g. GPS)
- "Data-fication" of the world (Big Data, open data, IoT... Much of this has a spatial footprint)
- Increase in: computational power + storage + open source

Some processes of interest for social scientists have a strong spatial dimension →

*where*is a legitimate question in itself and is at the heart of the mechanisms that explain them. For example:- Residential population distribution and (lack of) mixing
- Employment (urban centers, regional concentration of industries...)
- Income
- ...

**Non-spatial**techniques completely ignore this aspect and do not provide tools to gain insight about issues where location plays a role**Spatial analysis**provides a set of statistical tools that expand the amount of insight to be learnt from a given dataset, beyond what non-spatial methods allow for

Inter-dependence mediated through space

- Spatial randomness
- Positive spatial autocorrelation
- Negative spatial autocorrelation

- Completely random allocation of values across space
- Space plays no role whatsoever
- Traditional assumption in the non-spatial world but the exception rather than the rule in practice

- Closer values are more similar to each other than further ones
- Tobler's first law of Geography
- Present in many social science phenomena

- Closer values are more
*dissimilar*to each other than further ones - Harder to interpret, but associated with spatial competition
- Example: retail location

→ **Demo** lattice

**Dependence**→ Interaction, interdependence**Heterogeneity**→ Intrinsic characteristics unevenly distributed over space- With a cross-section, hard (impossible) to tell whether outcomes arise from interaction or from intrinsic individual characteristics
Spatial dependence Vs. Spatial heterogeneity

- Positive spatial autocorrelation → spatial difussion / spillovers
- Negative spatial autocorrelation → spatial competition

Same problem as in social networks: intrinsic individual characteristics or personal interaction (see this video for a great explanation)?

Spatial Data, Analysis and Regression - A mini course by Dani Arribas-Bel is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.