[Paper Review] Graphical outputs and Spatial Cross-validation for the R-INLA package using INLAutils

Tim Lucas, André Python+1 more|arXiv (Cornell University)|Apr 5, 2020

Soil Geostatistics and Mapping17 references4 citations

TL;DR

This paper introduces INLAutils, an R package that enhances R-INLA by providing intuitive graphical summaries and spatial leave-one-out cross-validation (SLOOCV) for Bayesian spatial models. It enables efficient visualization of model outputs via ggplot2 and automates predictive performance comparison across models using spatial cross-validation, with results showing overlapping MAE and RMSE intervals between models with and without spatial effects in the Meuse dataset.

ABSTRACT

Statistical analyses proceed by an iterative process of model fitting and checking. The R-INLA package facilitates this iteration by fitting many Bayesian models much faster than alternative MCMC approaches. As the interpretation of results and model objects from Bayesian analyses can be complex, the R package INLAutils provides users with easily accessible, clear and customisable graphical summaries of model outputs from R- INLA. Furthermore, it offers a function for performing and visualizing the results of a spatial leave-one-out cross-validation (SLOOCV) approach that can be applied to compare the predictive performance of multiple spatial models. In this paper, we describe and illustrate the use of (1) graphical summary plotting functions and (2) the SLOOCV approach. We conclude the paper by identifying the limits of our approach and discuss future potential improvements.

Motivation & Objective

• To address the challenge of interpreting complex R-INLA model outputs, which are stored as nested lists and difficult to navigate for non-expert users.
• To improve the model development workflow by providing accessible, customizable graphical summaries of R-INLA results using ggplot2.
• To implement a spatial leave-one-out cross-validation (SLOOCV) procedure that accounts for spatial autocorrelation in model evaluation.
• To enable direct comparison of multiple spatial models based on predictive performance metrics such as MAE and RMSE.
• To support researchers in assessing model fit and predictive accuracy in spatial Bayesian modeling with minimal coding overhead.

Proposed method

• The package extends R-INLA by implementing a custom autoplot method for INLA model objects, leveraging ggplot2 for flexible and customizable visualization of posterior marginals, predictions, and residuals.
• It introduces the ggplot_inla_residuals function to visualize residuals against fitted values, with added options for smoothing and standard error bands.
• The inlasloo function performs spatial leave-one-out cross-validation by iteratively removing observations within a user-defined radius around each left-out point, ensuring spatial dependence is respected.
• The method uses a spatial buffer (rad) around each left-out point to exclude nearby observations from training data, improving realism in predictive assessment.
• Predictive performance is evaluated using MAE and RMSE, with 95% confidence intervals computed via bootstrapping over the cross-validation iterations.
• The package supports multiple models and likelihood families (e.g., normal, binomial) in a single call, enabling side-by-side comparison of model performance.

Experimental results

Research questions

• RQ1 How can graphical summaries of R-INLA model outputs be made more accessible and customizable for non-expert users?
• RQ2 To what extent does spatial leave-one-out cross-validation improve the reliability of predictive performance assessment in spatial models compared to standard leave-one-out?
• RQ3 Can the SLOOCV procedure effectively distinguish between models with and without spatial random effects in real-world spatial datasets?
• RQ4 What is the computational cost of performing SLOOCV across multiple models using the INLAutils framework?
• RQ5 How do MAE and RMSE values compare between a model with a spatial component and one without, under spatial cross-validation?

Key findings

• The INLAutils package successfully implements a ggplot2-based interface for visualizing R-INLA model outputs, enabling users to easily inspect posterior marginals, predictions, and residuals with full customization.
• The inlasloo function enables efficient spatial cross-validation with a user-defined radius, ensuring that nearby observations are excluded during model fitting to reflect spatial dependence.
• In the Meuse dataset, both models—with and without spatial effects—showed overlapping confidence intervals for MAE and RMSE, indicating no statistically significant difference in predictive performance.
• The SLOOCV procedure took approximately 3–5 minutes to complete 20 iterations on a 64GB RAM Intel Xeon machine, demonstrating feasibility for large spatial datasets.
• The package supports multiple likelihood families and models in a single call, allowing direct comparison of predictive performance across different model formulations.
• The authors identify limitations, including the absence of likelihood-based predictive scores and the exclusion of spatio-temporal models, suggesting future extensions for broader applicability.