Models as Prediction Machines: How to Convert Confusing Coefficients into Clear Quantities Abstract Psychological researchers usually make sense of regression models by interpreting coefficient estimates directly. This works well enough for simple linear models, but is more challenging for more complex models with, for example, categorical variables, interactions, non-linearities, and hierarchical structures. Here, we introduce an alternative approach to making sense of statistical models. The central idea is to abstract away from the mechanics of estimation, and to treat models as βcounterfactual prediction machines,β which are subsequently queried to estimate quantities and conduct tests that matter substantively. This workflow is model-agnostic; it can be applied in a consistent fashion to draw causal or descriptive inference from a wide range of models. We illustrate how to implement this workflow with the marginaleffects package, which supports over 100 different classes of models in R and Python, and present two worked examples. These examples show how the workflow can be applied across designs (e.g., observational study, randomized experiment) to answer different research questions (e.g., associations, causal effects, effect heterogeneity) while facing various challenges (e.g., controlling for confounders in a flexible manner, modelling ordinal outcomes, and interpreting non-linear models).
Figure illustrating model predictions. On the X-axis the predictor, annual gross income in Euro. On the Y-axis the outcome, predicted life satisfaction. A solid line marks the curve of predictions on which individual data points are marked as model-implied outcomes at incomes of interest. Comparing two such predictions gives us a comparison. We can also fit a tangent to the line of predictions, which illustrates the slope at any given point of the curve.
A figure illustrating various ways to include age as a predictor in a model. On the x-axis age (predictor), on the y-axis the outcome (model-implied importance of friends, including confidence intervals). Illustrated are 1. age as a categorical predictor, resultings in the predictions bouncing around a lot with wide confidence intervals 2. age as a linear predictor, which forces a straight line through the data points that has a very tight confidence band and 3. age splines, which lies somewhere in between as it smoothly follows the data but has more uncertainty than the straight line.
Ever stared at a table of regression coefficients & wondered what you're doing with your life?
Very excited to share this gentle introduction to another way of making sense of statistical models (w @vincentab.bsky.social)
Preprint: doi.org/10.31234/osf...
Website: j-rohrer.github.io/marginal-psy...
