Peer-reviewed article
Mixture of Directed Graphical Models for Discrete Spatial Random Fields
J. Brandon Carter, Catherine A. Calder ·
Summary
Written by AI, not yet AICS's view · claude-sonnet-5-5This paper proposes a statistical method, a mixture of directed graphical models, for analysing discrete outcomes measured across neighbouring areas. The authors say it gives valid Bayesian results and is faster than exact Markov random field methods, and more principled than a commonly used approximation. They compare the method with existing approaches in simulations and in an analysis of ecometrics data from the Adolescent Health and Development in Context Study. The document is a methods paper and does not evaluate any intervention for children.
Key points
- The method is a mixture of directed graphical models whose components can be drawn as directed acyclic graphs and are quick to evaluate.
- The graphs are chosen to match an undirected graph of which areal units are spatially connected.
- It is presented as an alternative to Markov random fields, not an approximation of them.
- The authors introduce a concept of compatibility to build sets of directed graphs that keep the dependencies in the undirected template.
- The method is compared with Markov random fields and a popular approximation in simulations and in an analysis of ecometrics data from the Adolescent Health and Development in Context Study.
Limitations
The abstract does not report results, so it cannot tell us how well the method performs or what it finds about adolescent well-being. The child-related data are used only as an example application of a statistical method.
Abstract
Current approaches for modeling discrete-valued outcomes associated with spatially-dependent areal units incur computational and theoretical challenges, especially in the Bayesian setting when full posterior inference is desired. As an alternative, we propose a novel statistical modeling framework for this data setting, namely a mixture of directed graphical models (MDGMs). The components of the mixture, directed graphical models, can be represented by directed acyclic graphs (DAGs) and are computationally quick to evaluate. The DAGs representing the mixture components are selected to correspond to an undirected graphical representation of an assumed spatial contiguity/dependence structure of the areal units, which underlies the specification of traditional modeling approaches for discrete spatial processes such as Markov random fields (MRFs). Notably, the MDGM is not proposed as an approximation to an MRF, but rather as an alternative that provides valid posterior inference while being computationally faster than exact MRF inference and more principled than the pseudo-likelihood approximation (aMRF) commonly used in practice. We introduce the concept of compatibility to show how an undirected graph can be used as a template for the dependencies between areal units to create sets of DAGs which, as a collection, preserve the dependencies represented in the template undirected graph. Lastly, we compare highlighted classes of MDGMs to MRFs and a popular Bayesian MRF model approximation used in high-dimensional settings in a series of simulations and an analysis of ecometrics data collected as part of the Adolescent Health and Development in Context Study.