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Maximum Likelihood Estimation

Susumu Shikano
susumu.shikano@uni-konstanz.de

Universität Konstanz

Susumu Shikano is Professor of Political Methodology at the University of Konstanz. He is also affiliated with the Mannheim Centre for European Social Research and the Hanse Institute for Advanced Study in Delmenhorst.

His research interests are various topics in electoral politics, coalition formation and methodology.

Susumu has published articles in journals including Public Choice, Political Psychology, Party Politics, West European Politics, and the British Journal of Political Science.

  @SusumuShikano


Course Dates and Times

Friday 22 February 13:00–15:00 and 15:30–18:00

Saturday 23 February 09:00–12:30 and 14:00–17:30

Prerequisite Knowledge

Statistics, including regression models with different types of dependent variables.

Basic knowledge of R.


Short Outline

This course introduces maximum likelihood estimation (MLE), one of the most important methods for parameter estimation in modern social sciences, on which a large body of published empirical works relies.

You will learn the basic idea of MLE, and some of its extensions in several example cases.

In contrast to the least squares methods, MLE requires you to make some assumptions about distributions of stochastic terms. This course therefore also deals with basics of probability theory.

On the final afternoon you will write programs in R to estimate some model parameters.

Tasks for ECTS Credits
1 credit (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, class.


Long Course Outline

In modern social sciences, statistical analysis has long been established as an inference tool.

Although most published work relies on MLE for its statistical analysis, many researchers seem to be ignorant about MLE per se and rely instead on statistics software packages. Some interpret MLE results as if they were based on the least squares technique. Others cannot distinguish likelihood from probability.

This course, therefore, aims to deepen your understanding of how statistical packages use MLE. This will help you better understand inference, because MLE is closely related to the likelihood model of inference (King 1998).

We begin by discussing some important concepts:

  • likelihood
  • probability
  • uncertainty
  • inference.

Most importantly, we clarify likelihood and probability, and their distinct role in inference. We also look at foundations of probability theories, which many students learn only implicitly in conventional social science statistics lectures. These will help you understand the likelihood-based model of inference.

Using a linear regression example, you will also learn about computation of MLE (maximization algorithms) and their properties in inference statistics, in particular asymptotic ones.

After gaining a conceptual overview of MLE, you will learn how to program R to obtain MLE. R packages are available, so you won't have to program the maximization algorithms yourself, but you will learn how to define the likelihood function.

The course starts with a linear regression model and extends the classes of statistical model to discrete regression models, such as binary logit/probit and poisson models.

We cannot cover a wide range of statistical models in this short course, but after completing it, you should be able to apply the basic concept of MLE and program skills to various statistical models in different practical situations.

Day Topic Details
Saturday 9:00–10:30 & 11:00–12:30 (3 hours) Programming MLE in R

Introduction to MLE in R, linear regression models

Friday 13:00–15:00 & 15:30–18:00 (4.5 hours) Inference and MLE

The concept of likelihood and probability, probability theory, the likelihood model of inference, Newton-type algorithms in MLE, properties of MLE, linear regression models

Saturday 14:00–15:30 & 16:00–17:30 (3 hours) Applied MLE

Generalised linear models, model selection, R exercise

Day Readings
Friday

Gary King, Unifying Political Methodology: The Likelihood Theory of Statistical Inference 1998, Chapters 1–4

Henning Best and Christof Wolf, eds. The Sage Handbook of Regression Analysis and Causal Inference Sage, 2014; Chapter 2: Martin Elff, Estimation techniques: Ordinary least squares and maximum likelihood

Saturday Morning

Henning Best and Christof Wolf, eds. The Sage Handbook of Regression Analysis and Causal Inference Sage, 2014; Chapter 2: Martin Elff, Estimation techniques: Ordinary least squares and maximum likelihood

Saturday Afternoon

Gary King, Unifying Political Methodology: The Likelihood Theory of Statistical Inference 1998, Chapter 5

Software Requirements

Download R free if you do not already have it installed

Hardware Requirements

Please bring your own laptop

Literature

Henning Best and Christof Wolf, eds. The Sage Handbook of Regression Analysis and Causal Inference Sage, 2014; Chapter 2: Martin Elff, Estimation techniques: Ordinary least squares and maximum likelihood

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

Recommended Courses to Cover Before this One

<p style="text-align:left">Introduction to Statistics</p> <p style="text-align:left">Advanced Topics in Applied Regression</p> <p style="text-align:left">Multiple Regression</p> <p style="text-align:left">Introduction to R</p>

Recommended Courses to Cover After this One

<p style="text-align:left">Introduction to Bayesian inference</p> <p style="text-align:left">Multilevel Modelling</p> <p style="text-align:left">Panel Data Analysis</p> <p style="text-align:left">Advanced Discrete Choice Modelling</p> <p style="text-align:left">&nbsp;</p>


Additional Information

Disclaimer

This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed in due time.

Note from the Academic Conveners

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, contact the instructor before registering.