AIC Model Averaging with MuMIn and Hierarchical Bayesian Modelling with rstanarm
Published:
Statistical modelling in R, using lm, MuMIn and rstanarm.
Multiple regression and AIC model averaging
A regression of SARS-CoV-2 reproduction number on temperature, humidity, population density and intervention strength, on simulated data modelled after Smith et al. 2021 (PNAS).
Rather than fitting one model and reporting it, the candidate set was enumerated and averaged with MuMIn (dredge, model.avg), then extended with interaction terms. The interaction model won decisively, at AICc -56.3 against 8.4. The effects are not additive, and a model constrained to additivity would have reported confident, wrong coefficients.
Bayesian hierarchical modelling
A multilevel model fitted with rstanarm (stan_glmer, random intercept per group), compared against the same model with no random effects, using WAIC: 20.1 against 82.6, lower being better.
That gap is the cost of a specific mistake. When observations are grouped, treating them as independent is not a simplifying assumption but an error, and it inflates confidence in exactly the estimates you care about. The hierarchical model does not add flexibility for its own sake; it stops the model claiming more information than the data contain.