Susumu Shikano is Professor of Political Methodology. He is doing research on spatial models of politics and diverse topics in political behaviour. Before going to Konstanz, he was professor ad interim at the University of Potsdam (2008) and assistant professor at the University of Mannheim (2001-2008). He received a Dr. Phil (2001) and Venia Legendi (2007) for political science from the University of Mannheim.

Course Content

Students will learn about the basic idea of maximum likelihood estimation, which enables to estimate parameters of diverse kinds of statistical models, in particular generalized linear models (GLM). GLMs can have diverse kinds of outcome variables (e.g. binary, ordinal, unordered categorical, count, and duration ones) and explicitly model uncertainty based on a certain probability distribution corresponding to the property of the outcome variable at stake. In this course, students will learn about the probability and statistical theory behind maximum likelihood estimations and GLMs, how to estimate the parameters in R, and how to produce results that are elegant and understandable to a wide audience.

 

Course Objectives

In this course, students will learn:

• the basic idea and concepts of maximum likelihood estimation,
• important properties of maximum likelihood estimators,
• a wide variety of GLMs,
• how to set up statistical models for theories of interest and available data,
• how to obtain the estimates of model parameters,
• how to compare multiple statistical models,
• and how to present the estimated results.

 

Course Prerequisites

Participants should be able to accurately interpret a coefficient table of linear regression models and should be knowledgeable about the binary logit model. Participants should also know the basics for programming in R. A solid background in some math, especially logarithms, summations, and derivatives, is useful but not strictly required.

 

Representative Background Reading

Whitten, Guy D., and Harvey D. Palmer. “Heightening Comparativists’ Concern for Model Choice: Voting Behavior in Great Britain and the Netherlands.” American Journal of Political Science, vol. 40, no. 1, 1996, pp. 231–260.

Alvarez, R. Michael, and Jonathan Nagler. “When Politics and Models Collide: Estimating Models of Multiparty Elections.” American Journal of Political Science, vol. 42, no. 1, 1998, pp. 55–96.

 

Required texts

Gary King. 1998. Unifying Political Methodology: The Likelihood Theory of Statistical Inference. Ann Arbor, MI: University of Michigan Press.

Elff, Martin. 2014. “Estimation Techniques: OLS and MLE”. 7-30 in Regression Analysis and Causal Inference, ed. by Henning Best and Christoph Wolf. London: Sage.

This introduction to maximum likelihood estimation (MLE) deals with its theoretical background as well as application using R. The course will begin with the basic and intuitive idea of maximum likelihood estimation and its application in quite common research contexts such as analysis of binary data by using generalized linear models (GLM) (first three days). At this stage, the students will also learn how to use R-packages to obtain estimation results of GLM. For this purpose, example data and source codes will be provided by the instructor. This intuitive, but rather superficial understanding of MLE will be better founded by discussing its more theoretical backgrounds (Days 4-5). To assist students’ understanding of mathematical, statistical and computational backgrounds behind MLE, some R codes will be provided. Subsequently, we will discuss a wider variety of statistical models (Days 6-7) and learn what and how to present the results (Day 8). Also these stages will be accompanied with R exercises. After discussing some advanced topics concerning MLE (Day 9), we will close the course with some outlook toward some alternative estimation methods (Day 10). Students will have opportunities to set up models for their own research questions and datasets, to estimate the parameters and to present their results during their course. This course will cover a wide variety of statistical models, however students will obtain most important fundamental knowledge about MLE and GLM so that they will be able to set up and identify their own statistical model depending on their theoretical models and datasets.

Day-by-Day Program

Day 1: Basics

• Theoretical and statistical models, inference, and (parameter) estimation
• Motivating example: binary logit model
• The basic structure of generalized linear models
• Intuitive idea of maximum likelihood estimation

Readings:

King Chap 1-4 (required text)

Day 2: Models for binary outcome variables

• Binary logit/probit models
• Hand-rolled programming to obtain maximum likelihood estimates by using bbmle-package
• Interpretation of the results
• Relationship with theoretical models (random utility models)

Readings:

King Chap 5 (required text)

Day 3 Models for further discrete outcome variables I

• Ordered outcome variables
• Count outcome variables
• Programming by using glm-package

Readings:

King Chap 5 (required text)

Day 4 Fundamentals in maximum likelihood estimation I

• Essentials in the probability theory
• Likelihood function
• Computing the maximum of likelihood functions

Readings:

Elff (required text)

Day 5 Fundamentals in maximum likelihood estimation II

• Inferences
• Important properties of maximum likelihood estimators
• Differences from ordinary least squares (OLS)

Readings:

Elff (required text)

Day 6 Models for further discrete outcome variables II

• Multinomial and conditional logit models
• Relationship with binary logit
• Multinomial probit

Core readings: Alvarez and Nagler (representative background reading)

Day 7 Models for continuous outcome variables

• Duration models
• Models for proportions
• Robust regression models

Readings:

Box-Steffensmeier, Janet M., and Christopher Zorn. 2002. Duration Models for Repeated Events. Journal of Politics 64: 1069-1094.

Jonathan Katz and Gary King. 1999. “A Statistical Model for Multiparty Electoral Data.” American Political Science Review, 93, Pp. 15–32.

Day 8 Presentation of the results

• Model selection with the likelihood ratio test and information criteria
• Presentation in a table
• Visual presentation

Readings:

King Chap 4-5 (required text)

Day 9: Advanced topics concerning maximum likelihood estimation

• Restricted maximum likelihood
• Application: Multilevel models with few clusters
• Expectation–maximization algorithm as solution for missing values/latent variables
• Application I: MLE with missing values
• Application II: Binary probit model

Readings:

Elff (required text)

Elff, Martin, Heisig, Jan Paul, Schaeffer, Merlin, Shikano, Susumu: Multilevel Analysis with Few Clusters: Improving Likelihood-based Methods to Provide Unbiased Estimates and Accurate Inference, British Journal of Political Science, Forthcoming.

Jackman, Simon: Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo, American Journal of Political Science, Vol.44,No.2,2000, pp.369-98.

Day 10: Concluding sessions

• Beyond maximum likelihood estimators
• Student presentations

Readings:

Jackman, Simon: Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo, American Journal of Political Science, Vol.44,No.2,2000, pp.369-98.