Intro to GLM: Binary, Ordered and Multinomial Logistic, and Count Regression Models

Political 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 usual technique employed to tackle with some common types of non-continuous dependent variables, namely generalized linear modeling (GLM). By reflecting on the type of data generating process behind the observed outcomes, the course aims to make the students comfortable with concepts such as linear predictor, link function, and maximum likelihood. Moreover, by relying on statistical simulation as well as real-world data, the course will provide students with some tools to generate and report quantities of interest obtained via GLM regressions.

The course starts in medias res, discussing the most simple and common example where GLM is needed, namely binary response variables. Students will be encouraged to discuss what potential problems 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. Then, the course focuses on issues arising from the interpretation of the coefficients. In this part, we will discuss some strategies to obtain  quantities of interest (i.e. predicted probabilities) and visualize them in a compelling way. This will include the interpretation of interaction terms, and the graphic presentation of interaction effects. In the last two days, the course covers three less common but nevertheless important types of outcome variables: ordinal, categorical, and counts. On the fourth day, ordinal and multinomial logit models are discussed, as a generalization of the framework introduced in the study of binary outcomes. On the fifth day, the focus moves to poisson and negative binomial regression models.

The lab sessions will be based on the open-source statistical software R (www.r-project.org). Because several functions will require the use of additional packages, it is recommended that the students bring their own laptops, so that the download and installation of additional components will proceed smoothly. The lecturer will provide all the datasets necessary for the lab exercises.

The course assumes a basic understanding of descriptive statistics and probability theory (e.g. types of variables, basic statistics, common distributions) and some proficiency with linear regression analysis (i.e. how to interpret an OLS output). Moreover, the course will assume some familiarity with R. Note that this is not an introductory course to R. Although the lecturer will be open to explain and discuss the code used for the exercises, it is assumed that the students can move within the R environment with a certain degree of confidence.

a) Participants should have taken the course on “Multiple Regression Analysis: Estimation and Diagnostics” in the first week of the summer school or have obtained equivalent prior knowledge through other means. (the coruse might have a different title this year, please check)

b) The course relies heavily on the software R: students will be given examples of some rather abstract concepts like ”maximum likelihood” or ”data generating process” by means of statistical simulation. While this can be a very helpful tool, it requires that the students have a basic understanding of the R language. For students unfamiliar with R, a preparatory course will be offered prior to the first week. Otherwise, online resources are plenty. I recommend the tutorial ”Try R”, available online for free (http://tryr.codeschool.com/) and/or the ”Foundations” section of the online tutorial by Hadley Wickham (http://adv-r.had.co.nz/). A good introduction book is “R in a Nutshell – A Desktop Quick Reference” by Joseph Adler (O’Reilly, 2010).

c) Students are expected to understand the logic of inferential statistics. Students familiar with R but in need of a refresher in basic statistics are encouraged to take part in the preparatory course on statistics.

d) The course will use some matrix algebra notation, hence the student should have some familiarity with the logic of matrix algebra.