Margins of Error or Insight? The Step After Regression

Over the holidays, I’ve been busy working on a paper advocating the introduction of estimated marginal means to students and practitioners—an essential yet often overlooked step following regression analysis. Many individuals, whether trained in regression through formal courses or required to use it professionally, often feel uncertain about their grasp of regression models. In my 30+ years of working with regression analysis, I’ve encountered more instances of incorrect applications or misinterpretations than I’d like to admit. Truth be told, I have made my fair share of mistakes with regression!

Estimated marginal means—commonly referred to as marginal means—can significantly enhance the understanding and utility of regression analysis. If you’re comfortable running regressions but are puzzled by the output, marginal means could be the key to unlocking more precise insights.

So, what exactly are marginal means? At their core, marginal means are conditional means that account for the other variables in your regression model. Consider an example: you want to analyze wage differences between men and women while controlling for factors such as years of experience, education level, type of education, productivity measures, and other variables that might influence compensation.

The goal is to determine whether, after holding all other relevant factors constant, there remains a significant difference between the wages of men and women.

Marginal means readily estimate the average wages for men and women under the same conditions, making it far easier to explain and interpret the results. This is often simpler and more intuitive than deciphering regression coefficients directly from the output.

Recently, I came across an excellent video by Dr. Yury Zablotski in Germany that visually illustrates this concept in a clear and compelling way. If the idea of marginal means feels abstract or unfamiliar, I highly recommend the video linked below—it provides the best visual introduction I’ve found to date.

https://youtu.be/cqmMNR6x73g

For a comprehensive guide on estimated marginal means in Stata, refer to the following manual: Stata Margins Manual (PDF).

If you primarily work with R, Dr. Russell V. Lenth has developed a series of insightful vignettes for his emmeans package. These resources provide detailed explanations and practical examples. Explore them here: emmeans Package on CRAN.

If you are interested in reviewing the draft of my paper and might be tempted to provide feedback, email me at [email protected].