Bayesian CAR Models for Road-Segment Traffic

Tools for simulating and modeling traffic flow on road networks using spatial conditional autoregressive (CAR) models. The package represents road systems as graphs derived from 'OpenStreetMap' data < https://www.openstreetmap.org/> and supports network-based spatial dependence, basic preprocessing, and visualization for spatial traffic analysis.

trafficCAR

Overview

trafficCAR is an R package for constructing conditional autoregressive (CAR) precision matrices on graph and road network data. It is built for users seeking principled spatial dependence structures for linear networks (streets, paths, and segmented roadways) and end-to-end utilities for turning raw road geometries into model-ready adjacency/weight matrices.

The package is designed to support methodological, simulation-based, and applied modeling workflows with intrinsic and proper CAR models defined on network structures. It includes helpers for turning LINESTRING/MULTILINESTRING features into stable segments, for building graph objects and sparse matrices, and for scaling or constraining CAR precision matrices to align with common spatial statistics conventions.

Core functionality includes:

• Building graph representations from spatial road geometries

• Constructing adjacency and weight matrices

• Generating ICAR and proper CAR precision matrices

In addition, trafficCAR provides convenient wrappers and plotting utilities aimed at traffic and speed modeling, so you can fit CAR/ICAR models and immediately map latent effects back to a road network.

What the package offers

• Road and graph preparation: Convert LINESTRING/MULTILINESTRING road data to stable segment IDs with lengths (roads_to_segments()), construct segment adjacency (build_adjacency()), and build a full igraph-based road network (build_network()).

• Spatial weights and precision matrices: Create binary or row-standardized weight matrices (weights_from_adjacency()), build intrinsic and proper CAR precision matrices (car_precision()), apply Besag scaling (intrinsic_car_precision()), and impose sum-to-zero constraints for ICAR components (icar_sum_to_zero()).

• Simulation utilities: Sample from proper CAR latent Gaussian models with Gibbs updates (sample_proper_car()) or draw from multivariate normals with sparse precision matrices for custom workflows (rmvnorm_prec()).

• Model fitting for traffic outcomes: Fit Gaussian CAR/ICAR regression models with optional covariates (fit_car()), or use traffic-oriented wrappers that prepare speed and travel-time outcomes, apply transformations, and return augmented fit objects (fit_traffic()).

• Augmentation and visualization: Attach fitted latent effects back to road geometries for mapping (augment_fit() and augment_traffic_fit()), create static plots (plot_traffic_static()), and generate interactive leaflet maps (plot_traffic_interactive()).

• Helper utilities: Simplify road geometries while preserving topology (simplify_roads()), compute connected components for ICAR centering (components_from_adjacency()), and derive degree or row-standardized matrices used across the CAR constructors.

Typical workflow

1. Prepare road geometries: Clean and optionally simplify input road data. Convert LINESTRING/MULTILINESTRING features into stable, length-aware segments with roads_to_segments().

2. Build network structure: Use build_adjacency() or build_network() to produce adjacency/graph objects that encode which road segments touch or intersect.

3. Create weights/precision matrices: Convert adjacency into binary or row-standardized weights (weights_from_adjacency()), then build ICAR or proper CAR precision matrices with car_precision() or intrinsic_car_precision().

4. Fit models or simulate: Fit Gaussian CAR/ICAR regression models with fit_car() or fit_traffic(), or run simulations with sample_proper_car() and rmvnorm_prec() for benchmarking and model checking.

5. Augment and visualize: Attach fitted spatial effects back to the road geometries (augment_fit() or augment_traffic_fit()) and visualize results via static or interactive plotting helpers.

Data expectations

• Road geometries should be LINESTRING or MULTILINESTRING features, typically stored in sf objects.
• Segment-level outcomes or covariates should align with the segments produced by roads_to_segments() or with the graph indices used to build adjacency/weight matrices.
• For ICAR models, connected components are handled via components_from_adjacency() and sum-to-zero constraints can be applied with icar_sum_to_zero().

Installation

You can install the released version of trafficCAR from CRAN:

install.packages("trafficCAR")

To install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("mell00/trafficCAR")