directed cyclic graph (DCG)
Definition
A directed cyclic graph (DCG) is a causal graphical model in which directed edges between variables form at least one cycle, meaning that a variable can be both a cause and an effect of another variable within the same graph. This distinguishes a DCG from a directed acyclic graph (DAG), where no such cycles are permitted. A DCG is suited to representing feedback loop relationships, such as the reciprocal causal relationship X2 causes X3 and X3 causes X2, which cannot be encoded in a DAG. Cyclic causal models fit to cross-sectional data may be interpreted as reflecting causal relations between the equilibrium states of a dynamic system, making them appropriate for psychological phenomena such as psychopathology, where feedback loops between symptoms are theoretically expected.
Sources: Park et al. (2024)
Related Terms
- constraint-based (1 shared article)
- cyclic causal discovery (1 shared article)
- partial ancestral graph (PAG) (1 shared article)
- statistical network model (1 shared article)
Applications
Directed Cyclic Graph (DCG) and Directed Acyclic Graph (DAG)
A DAG consists of directed edges with no cycles, whereas a DCG allows cycles among its vertices. This structural difference has direct consequences for causal inference: a pattern of statistical dependence that identifies a direct causal link in a DAG may not reflect a direct causal link in a DCG, making the interpretation of DCG output considerably more demanding. Additionally, all acyclic path models are statistically identified, a guarantee that does not extend to path models containing cycles.
Sources: Park et al. (2024)
Directed Cyclic Graph (DCG) and Constraint-based Causal Discovery
Constraint-based causal discovery methods use patterns of statistical dependence and independence in observational data to infer causal structure, and some of these methods have been extended to handle cyclic graphs. Park et al. examine three such algorithms and find, through simulation, that an autoregressive-based method outperforms FCI-variants and latent-variable-based methods when recovering DCG structures from psychologically plausible data. The performance of these methods varies with sample size, network density, and the presence of unobserved confounders.
Sources: Park et al. (2024)
Directed Cyclic Graph (DCG) and Pairwise Markov Random Field (PMRF)
A PMRF is an undirected graphical model in which edges represent conditional statistical associations, and it stands in contrast to a DCG, which encodes directed causal relationships including feedback loops. Each DCG implies a corresponding PMRF, but the undirected edges of the PMRF do not carry causal direction and cannot distinguish the cyclic structure present in the underlying DCG. This means that statistical network models based on the PMRF are likely to perform poorly as tools for recovering the kind of cyclic causal structure represented by a DCG.
Sources: Park et al. (2024)
