Marginality principle

[2025-05-19]

Image from Morris, Smeden and Pham, 2023

In a linear mixed model framework, the marginality principle applies only to the fixed effects, simply because of the way the X matrix is defined, i.e. via dummy encoding with 1 less factor level or df = p-1 per factor. Excluding the main effects when the interaction effect is included makes it impossible to extract all the effects of the interaction term.