# Regression Analysis for Spatial Data

**Prerequisites (knowledge of topic)**

Students should be interested in spatial topics such as real estate markets, urban economics, crime, pollution, spatial distribution of political preferences, and trade flows. We assume that students are familiar with matrix algebra, and have had courses in probability theory and econometrics. The course emphasizes programming and empirical application. The empirical implementation of spatial models is done in R, hence some familiarity in R is useful but not required for the course. The course is open to students from the PiF/PEF and other external PhD programs.

**Learning objectives**The goal of this course is to provide students with the main tools for analyzing and visualizing spatial data. Students will learn how to estimate and interpret a range of spatial models and how to program own models in R.

**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**

*Monday*

**Lecture 1: 09:15 ‑ 12:00**

R Tutorial 1: 13:00 ‑ 15:00

*Tuesday*Lecture 2: 09:15 ‑ 12:00

R Tutorial 2: 13:00 ‑ 15:00

*Wednesday*

Lecture 3: 09:15 ‑ 12:00

R Tutorial 3: 13:00 ‑ 15:00

*Thursday*

Lecture 4: 09:15 ‑ 12:00

R Tutorial 4: 13:00 ‑ 15:00

*Friday*

Lecture 5: 09:15 ‑ 12:00

R Tutorial 5: 13:00 ‑ 15:00*Times and room information in the timetable apply.*

**Literature**

**Mandatory**

LeSage, J., and R.K. Pace (2009), ʺIntroduction to Spatial Econometricsʺ. CRC Press.

**Supplementary / voluntary**

Elhorst, J.P. (2014), ʺSpatial Econometrics: From Cross‑Sectional Data to Spatial Panelsʺ, Springer.

Holly, S., M.H. Pesaran, and T. Yamagata (2011), ʺThe Spatial and Temporal Diffusion of House Prices in the UKʺ,*Journal of Urban Economics *69, 2‑23.

LeSage, J. (2014), ʺWhat Regional Scientists Need to Know about Spatial Econometricsʺ,*The Review of Regional Studies *44, 13‑32.

Examination part

Examination paper written at home (100%)

Remark: Paper Replication or own research idea.

**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.

**Examination relevant 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.