Prepare data for ICAR models

Source: R/convenience-functions.R

Given a symmetric n x n connectivity matrix, prepare data for intrinsic conditional autoregressive models in Stan. This function may be used for building custom ICAR models in Stan. This is used internally by stan_icar.

prep_icar_data(C, scale_factor = NULL)

Source

Besag, Julian, Jeremy York, and Annie Mollié. 1991. “Bayesian Image Restoration, with Two Applications in Spatial Statistics.” Annals of the Institute of Statistical Mathematics 43 (1): 1–20.

Donegan, Connor. Flexible Functions for ICAR, BYM, and BYM2 Models in Stan. Code Repository. 2021. Available online: https://github.com/ConnorDonegan/Stan-IAR/ (accessed Sept. 10, 2021).

Freni-Sterrantino, Anna, Massimo Ventrucci, and Håvard Rue. 2018. “A Note on Intrinsic Conditional Autoregressive Models for Disconnected Graphs.” Spatial and Spatio-Temporal Epidemiology 26: 25–34.

Morris, Mitzi, Katherine Wheeler-Martin, Dan Simpson, Stephen J Mooney, Andrew Gelman, and Charles DiMaggio. 2019. “Bayesian Hierarchical Spatial Models: Implementing the Besag York Mollié Model in Stan.” Spatial and Spatio-Temporal Epidemiology 31: 100301.

Riebler, Andrea, Sigrunn H Sørbye, Daniel Simpson, and Håvard Rue. 2016. “An Intuitive Bayesian Spatial Model for Disease Mapping That Accounts for Scaling.” Statistical Methods in Medical Research 25 (4): 1145–65.

Arguments

C

Connectivity matrix

scale_factor

Optional vector of scale factors for each connected portion of the graph structure. If not provided by the user it will be fixed to a vector of ones.

Value

list of data to add to Stan data list:

k

number of groups

group_size

number of nodes per group

n_edges

number of connections between nodes (unique pairs only)

node1

first node

node2

second node. (node1[i] and node2[i] form a connected pair)

weight

The element C[node1, node2].

group_idx

indices for each observation belonging each group, ordered by group.

m

number of disconnected regions requiring their own intercept.

A

n-by-m matrix of dummy variables for the component-specific intercepts.

inv_sqrt_scale_factor

By default, this will be a k-length vector of ones. Placeholder for user-specified information. If user provided scale_factor, then this will be 1/sqrt(scale_factor).

comp_id

n-length vector indicating the group membership of each observation.

Details

This is used internally to prepare data for stan_icar models. It can also be helpful for fitting custom ICAR models outside of geostan.

Examples

data(sentencing)
C <- shape2mat(sentencing)
icar.data.list <- prep_icar_data(C)