# Regression Analysis for Spatial Data

**Work load**

Classes: 12 sessions (90 minutes): 6 lecture sessions and 6 R Tutorials

Assignments: Two graded R assignments to be solved individually. About 5 hours for each assignment.

Paper Replication: About 10 hours.

**Prerequisites**

Students are expected to have basic knowledge of probability theory, econometrics, and matrix algebra. The course is based on the program R. We ask students to bring their laptops to class. R and R Studio are available for free on Windows computers and Macs.

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**Course content**

This course focuses on the visualization and modeling of spatial data. Examples are taken from different research areas such as political science, empirical international trade, criminology, and real estate. It offers a detailed explanation of individual estimation methods and their implementation in R. In this course, students will learn

- How to generate a variety of different maps that visualize the location of spatial units
- How maximum likelihood estimation works and how to set up and optimize a likelihood function in R
- How to deal with computational problems that are frequently accounted when working with spatial data
- How to increase computation speed using concentrated maximum likelihood and the matrix exponential spatial specification model
- How to estimate a spatial regression model both, with cross-sectional and with time-series data
- How to properly interpret the output from a spatial regression model and how to investigate policy interventions.
- A basic background on spatial interaction models, heterogeneous coefficient SAR models, and spatio-temporal models

What students do NOT learn in this course:

- Estimation of spatial regression models with other estimation techniques such as IV, NLS, and Bayesian Methods
- The use of a specialized Geographic Information System such as ArcGIS

**Structure**

*Day 1*

Lecture 1: 09:15 – 12:00

R Tutorial 1: 13:00 – 15:00

*Day 2*

Lecture 2: 09:15 – 12:00

R Tutorial 2: 13:00 – 15:00

*Day 3*

Lecture 3: 09:15 – 12:00

R Tutorial 3: 13:00 – 15:00

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*Day 4*

Lecture 4: 09:15 – 12:00

R Tutorial 4: 13:00 – 15:00

*Day 5*

Lecture 5: 09:15 – 12:00

R Tutorial 5: 13:00 – 15:00

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**Literature**

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**Mandatory**

LeSage, J., and R.K. Pace (2009), “Introduction to Spatial Econometrics”. CRC Press.

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**Supplementary / voluntary**

Elhorst, J.P. (2014), “Spatial Econometrics: From Cross-Sectional Data to Spatial Panels”, Springer.

Holly, S., M.H. Pesaran, and T. Yamagata (2011), “The Spatial and Temporal Diffusion of House Prices in the UK”, *Journal of Urban Economics *69, 2–23.

LeSage, J. (2014), “What Regional Scientists Need to Know about Spatial Econometrics”, *The Review of Regional Studies* 44, 13–32.

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**Mandatory readings before course start**

None

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**Examination part**

The course contains two graded R assignments and one graded paper replication. The assignments and the paper replication are to be solved individually.

R Assignment 1: 20%

R Assignment 2: 20%

Paper Replication: 60%

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**Supplementary aids**

For solving the R assignments and the paper replication, any source from academic papers, text books and other sources from the internet are allowed.

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**Examination content**

- SAR model, SDM model, CML, MESS, Spatial Interaction model, Spatial Panel model, HSAR model
- Implementing maximum likelihood estimation in R: Full Maximum Likelihood, Concentrated Maximum Likelihood, Matrix Exponential Spatial Specification.

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**Literature**

- LeSage, J., and R.K. Pace (2009), “Introduction to Spatial Econometrics”. CRC Press, Chapter 1, 2, 3, 4, 8, and 9.
- LeSage, J., and Y.-Y. Chih (2016), “Interpreting Heterogeneous Coefficient Spatial Autoregressive Panel Models”,
*Economics Letters*142, 1–5.