A note on Bayesian R-squared for generalized additive mixed models
Methodology
2024-10-21 v1
Abstract
We present a novel Bayesian framework to decompose the posterior predictive variance in a fitted Generalized Additive Mixed Model (GAMM) into explained and unexplained components. This decomposition enables a rigorous definition of Bayesian . We show that the new definition aligns with the intuitive Bayesian proposed by Gelman, Goodrich, Gabry, and Vehtari (2019) [\emph{The American Statistician}, \textbf{73}(3), 307-309], but extends its applicability to a broader class of models. Furthermore, we introduce a partial Bayesian to quantify the contribution of individual model terms to the explained variation in the posterior predictions
Cite
@article{arxiv.2410.14002,
title = {A note on Bayesian R-squared for generalized additive mixed models},
author = {Abdollah Jalilian and Aki Vehtari and Luigi Sedda},
journal= {arXiv preprint arXiv:2410.14002},
year = {2024}
}