Path weights in concentration graphs

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• dc.contributor.author Roverato, Alberto
• dc.contributor.author Castelo Valdueza, Robert
• dc.date.accessioned 2023-01-19T06:56:02Z
• dc.date.available 2023-01-19T06:56:02Z
• dc.date.issued 2020
• dc.description.abstract A graphical model provides a compact and efficient representation of the association structure in a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and higher-order graphical structures such as cliques or paths. Typically, paths play a central role in these models because they determine the dependence relationships between variables. However, while a theory of path coefficients is available for directed graph models, little research exists on the strength of the association represented by a path in an undirected graph. Essentially, it has been shown that the covariance between two variables can be decomposed into a sum of weights associated with each of the paths connecting the two variables in the corresponding concentration graph. In this context, we consider concentration graph models and provide an extensive analysis of the properties of path weights and their interpretation. Specifically, we give an interpretation of covariance weights through their factorization into a partial covariance and an inflation factor. We then extend the covariance decomposition over the paths of an undirected graph to other measures of association, such as the marginal correlation coefficient and a quantity that we call the inflated correlation. Application of these results is illustrated with an analysis of dietary intake networks.
• dc.format.mimetype application/pdf
• dc.identifier.citation Roverato A, Castelo E. Path weights in concentration graphs. Biometrika. 2020;107(3):705-22. DOI: 10.1093/biomet/asaa010
• dc.identifier.doi http://dx.doi.org/10.1093/biomet/asaa010
• dc.identifier.issn 0006-3444
• dc.identifier.uri http://hdl.handle.net/10230/55333
• dc.language.iso eng
• dc.publisher Oxford University Press
• dc.relation.ispartof Biometrika. 2020;107(3):705-22
• dc.rights © Oxford University Press. This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record Roverato A, Castelo E. Path weights in concentration graphs. Biometrika. 2020;107(3):705-22. DOI: 10.1093/biomet/asaa010 is available online at: https://doi.org/10.1093/biomet/asaa010.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Covariance decomposition
• dc.subject.keyword Concentration graph
• dc.subject.keyword Inflation factor
• dc.subject.keyword Partial correlation
• dc.subject.keyword Undirected path
• dc.subject.keyword Undirected graphical model
• dc.title Path weights in concentration graphs
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion