Takeaways from 'On the uses and abuses of regression models'

This weekend I found an interesting new preprint by Carlin and Moreno-Betancur on arxiv titled “On the Uses and Abuses of Regression Models” so I had to check it out.

The article focuses on medical literature, where regressions – even in my experience – often seem done almost automatically and then interpreted depending on the the desired question as opposed to with respect to model construction. “Garbage can” regressions to find “important risk factors” abound, as do repeat fittings of simple models in an attempt to describe a joint distribution. One of my favorite examples to show in class of the issues with the latter is a 2008 paper by Wang et al. that to date has been cited more than 1,000 times. The topic of the paper is an analysis of NHANES data with the aim of predicting the prevalence of obesity in the US. They desire to describe how different subgroups of Americans, that is the different genders and ethnicities, fare. Instead of fitting a joint model, they fit multiple linear models. This leads to fun results in their Table 2, where all Americans of all races and ethnicities will be obese by 2048, yet all men won’t be obese until 2051. Mexican-American men fare the best, as they escape being part of all Americans somehow and won’t reach 100% prevalence until 2126.

Carlin and Moreno-Betancur describe these and other issues they encountered in the literature. One I find notable is what they call the “true model myth.” Essentially, the idea that that the “best” fitted model represents the data generating process, ergo the coefficients are easily interpreted in a causal manner so we can derive practice recommendations from these models without much discussion. That is of course not accurate.

Overall, Carlin proposes a simple classification scheme for the different purposes of a regression analysis:

1. “descriptive:” characterise the distribution of a feature or health outcome in a population,
2. “predictive:” produce a model or algorithm for predicting future values given certain predictors,
3. “causal:” investigate the extent to which a health outcome in some population would be different if a particular intervention were made.

Since they understand the problem with the misuse and misinterpration of regression to (at least partially) be due to a certain vagueness with respect to the purpose for which the regression is fit, they propose a teaching framework centered around these types of research questions. This is in opposition of the more “traditional” focues on the “maths” of the problem. In other words, focus more on using standard tools to answer specific questions, than learning how to do simple problems “by hand” and then hoping that eventually people will figure out the hard parts of applying the theory to real life on their own.

Overall, I think the paper is a worthwhile read. It reminds me of two other books I like that take a model-centric approach to teaching regression methos – McElreath’s “Statistical Rethinking” and “Regression and Other Stories” by Gelman, Hill, and Vehtari. Gelman also posted about this preprint on his blog. Check out the discussion section there for other good insights and some additional reading material on this topic.