Introduction to Logistic Regression and General Linear Models: Binary, Ordered, Multinomial and Count Outcomes

Scientists are often interested in studying outcome variables that are not linear in nature. For instance, scholars may be interested in studying discrete choices among two or more options (e.g. voting or abstaining, choosing party X instead of party Y or Z, etc.) or the number of times a particular event is repeated (e.g. in how many wars a country was involved over a given period of time). In these cases, using OLS regression may produce biased or even meaningless results.

This course is meant to provide an introduction to a common technique for tackling some common types of non-continuous dependent variables, namely generalised linear modelling (GLM). By reflecting on the type of observed outcomes, with the use of real-world data, the course will enable you to report, explain and interpret quantities of interest via GLM regressions.

Each day is divided to two parts. The first is a lecture about the day’s topic and the second a lab session, where we see the theory in practice on real-world datasets. Modelling techniques of GLM are explained and applied by exercises using free access social science data, or you can use your own data for analyses. Daily assignments allow the application and transfer of GLM methodology to your own research interests.

The course starts in medias res, discussing the most simple and common example where GLM is needed, namely binary response variables. We will discuss the problems that may arise when applying linear regression to dichotomous variables, which assumptions are violated, and why it matters. With this example in mind, the course proceeds with a general introduction to the logic of GLM and to the Maximum Likelihood method to estimate models in the GLM framework.

The course focuses on issues arising from the interpretation of coefficients. In this part, we will discuss strategies to obtain quantities of interest (i.e. predicted probabilities). The course also covers three other types of outcome variables: ordinal, categorical, and counts. Ordinal and multinomial logit models will be discussed, as a generalisation of the framework introduced in the study of binary outcomes. Focusing on count variables, I will introduce poisson and negative binomial regression models.

Lab sessions will be based on the open-source statistical software R. I will therefore assume you can move within the R environment with a certain degree of confidence.

Because several functions will require the use of additional packages, I recommend you bring your own laptop, so the download and installation of additional components will proceed smoothly. I will provide all the datasets necessary for the lab exercises.

The course also assumes a basic understanding of descriptive statistics and probability theory (e.g. level of measurement of variables, basic statistics, common distributions) and the understanding of OLS regression analysis.

You should have a deep understanding of Ordinary Least Squares (OLS) regression or have taken the Week 1 course Multiple Regression Analysis: Estimation, Diagnostics, and Modelling or have obtained equivalent prior knowledge through other means.

You should have some familiarity with using the software R to manage data.

If you are unfamiliar with R, I recommend you take Akos Mate's preparatory course R Basics prior to the first week. Otherwise, online resources are plentiful, including:

DataCamp Introduction to R Course

PluralSight Courses in R

A website with tutorial and examples

A good introductory book is R in a Nutshell – A Desktop Quick Reference by Joseph Adler (O’Reilly, 2010)