# Multivariate regression in political science

I saw a new study published in Journal of Conflict Resolution. Here is a part of the abstract I found interesting: “Offering a first quantitative test of domestic drivers of transnational repression, using multivariate regression analysis, the paper finds that as repression intensifies domestically, the likelihood of that state subsequently escalating its transnational repression also increases substantively.”

When I see researchers promise a “multivariate regression analysis”, I always check whether the study is 1) interested in multiple dependent variables or 2) is actually talking about a multivariable regression analysis. I always hope for the first, but it most often turns out the latter is the case.

Here is a good description from Mustillo et al. (2018) on the difference between multivariate and multivariable:

Scholars from many disciplines use these terms interchangeably to describe their models, but they do not mean the same thing. Sociologists are not alone in this common practice. Using them interchangeably can cause confusion as to what kind of model is actually being estimated.

Simple regression refers to a model with one independent variable and one dependent variable. Multiple regression refers to a model with multiple independent variables and one dependent variable. Another term for multiple regression is multivariable regression.

A multivariate model is an entirely different model from those mentioned above: a multivariate model is a model with multiple dependent variables, such as factor analysis, a structural equation model, or a latent growth curve model. Given how often these terms are confused in published work, many argue that the distinction has become arbitrary or semantic, but we think it is important to maintain the distinction given that multivariate statistics is a well-developed branch of statistics in its own right, often the subject of entire courses, and it is consistent with usage in other fields. This is important, since ASR papers are read widely across the social sciences, not just sociology.

I agree that it is important to maintain the distinction between multivariate and multivariable regression. Out of curiosity, I had a quick look at recent studies (i.e., from this year) published in the American Political Science Review mentioning “multivariate”.

The search returned six studies in total (eight if you do not include papers citing “multivariate”). From what I can see, most of the studies talk about multivariate but mean multiple regression, i.e., Adams et al. (2023), Lublin and Wright (2023), Mathisen (2023), Reiljan et al. (2023), and Thesen and Yildirim (2023). Rodriguez et al. (2023) is, from what I can see, the only study that is not using the terms interchangeably and explicitly write “multivariate multiple regression model”.

As structural equation models and similar techniques are not as popular in political science as in other fields, it is maybe not a big surprise that political scientists do not care that much about precise statistical language and distinguish between ‘multivariate’ and ‘multiple’. However, I would like to see more political scientists not use the term ‘multivariate’ when they do mean ‘multiple’.