A note on Bayesian R-squared for generalized additive mixed models
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913552726491136 |
|---|---|
| author | Jalilian, Abdollah Vehtari, Aki Sedda, Luigi |
| author_facet | Jalilian, Abdollah Vehtari, Aki Sedda, Luigi |
| contents | 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 $R^{2}$. We show that the new definition aligns with the intuitive Bayesian $R^{2}$ 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 $R^{2}$ to quantify the contribution of individual model terms to the explained variation in the posterior predictions |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Bayesian R-squared for generalized additive mixed models Jalilian, Abdollah Vehtari, Aki Sedda, Luigi Methodology 62F15, 62J12, 62J20 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 $R^{2}$. We show that the new definition aligns with the intuitive Bayesian $R^{2}$ 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 $R^{2}$ to quantify the contribution of individual model terms to the explained variation in the posterior predictions |
| title | A note on Bayesian R-squared for generalized additive mixed models |
| topic | Methodology 62F15, 62J12, 62J20 |
| url | https://arxiv.org/abs/2410.14002 |