Interpreting Models: Coefficients, Marginal Effects or Elasticities?

I’ve spoken about interpreting models before. I think that this is the most important part of our work, communicating results. However, it’s one that’s often overlooked when discussing the how-to of data science. That’s why marginal effects and elasticities are better for this purpose than coefficients alone.

Model build, selection and testing is complex and nuanced. Communicating the model is sometimes harder, because a lot of the time your audience has no technical background whatsoever. Your stakeholders can’t go up the chain with, “We’ve got a model. And it must be a good model because we don’t understand any of it.”

Our stakeholders also have a limited attention span so the explanation process is two fold: explain the model and do it fast.

For these reasons, I usually interpret models for my stakeholders with marginal effects and elasticities, not coefficients or log-odds. Coefficient interpretation is very different for regressions depending on functional form and if you have interactions or polynomials built into your model, then the coefficient is only part of the story. If you have a more complex model like a tobit, conditional logit or other option, then interpretation of coefficients is different for each one.

I don’t know about your stakeholders and reporting chains: mine can’t handle that level of complexity.

Marginal effects and elasticities are also different for each of these models but they are by and large interpreted in the same way. I can explain the concept of a marginal effect once and move on. I don’t even call it a “marginal effect”: I say “if we increase this input by a single unit, I expect [insert thing here]” and move on.

Marginal effects and elasticities are often variable over the range of your sample: they may be different at the mean than at the minimum or maximum, for example. If you have interactions and polynomials, they will also depend on covarying inputs. Some people see this as added layers of complexity.

In the age of data visualisation, I see it as an opportunity to chart these relationships and visualise how your model works for your stakeholders.

We all know they like charts!

Elasticity and Marginal Effects: Two Key Concepts

One of the critical parts of building a great model is using your understanding of the problem and context. Choosing an appropriate model type and deciding on appropriate features/variables to explore based on this information is critical.

The two key concepts of elasticity and marginal effects are fundamental to an economic understanding of model building. This is something that can be overlooked for practitioners not coming from that background. Neither concept is difficult or particularly obtuse.

This infographic came about because I had a group of talented economics students at the masters’ level who had no econometric background, by and large. In a crowded course, I don’t have much time to expand on my favourite things. This was my take on explaining the concepts quickly and simply.

Elasticity infographic

For those very new to the concept, this explanation here is simple. Alternatively, if you’re interested in non-constant marginal effects and ways they can be used, check out this discussion.