{"data":{"id":"10.6084/m9.figshare.1209696.v3","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1209696.v3","prefix":"10.6084","suffix":"m9.figshare.1209696.v3","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"J. T. Gaskins","affiliation":[],"nameIdentifiers":[]},{"name":"M. J. Daniels","affiliation":[],"nameIdentifiers":[]},{"name":"B. H. Marcus","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Sparsity Inducing Prior Distributions for Correlation Matrices of Longitudinal Data"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2014,"subjects":[{"subject":"Science Policy"},{"subject":"Inorganic Chemistry"},{"subject":"FOS: Chemical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Chemical sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Biological Sciences"},{"subject":"Evolutionary Biology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Genetics"}],"contributors":[],"dates":[{"date":"2014-11-11","dateType":"Created"},{"date":"2016-01-19","dateType":"Updated"},{"date":"2014","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/10618600.2013.852553","relatedIdentifierType":"DOI"},{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.1209696","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["212353 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"For longitudinal data, the modeling of a correlation matrix \u003cb\u003e R\u003c/b\u003e can be a difficult statistical task due to both the positive definite and the unit diagonal constraints. Because the number of parameters increases quadratically in the dimension, it is often useful to consider a sparse parameterization. We introduce a pair of prior distributions on the set of correlation matrices for longitudinal data through the partial autocorrelations (PACs), which vary independently over (−1,1). The first prior shrinks each of the PACs toward zero with increasingly aggressive shrinkage in lag. The second prior (a selection prior) is a mixture of a zero point mass and a continuous component for each PAC, allowing for a sparse representation. The structure implied under our priors is readily interpretable for time-ordered responses because each zero PAC implies a conditional independence relationship in the distribution of the data. Selection priors on the PACs provide a computationally attractive alternative to selection on the elements of \u003cb\u003e R\u003c/b\u003e or \u003cb\u003e R\u003c/b\u003e\u003csup\u003e− 1\u003c/sup\u003e for ordered data. These priors allow for data-dependent shrinkage/selection under an intuitive parameterization in an unconstrained setting. The proposed priors are compared to standard methods through a simulation study and illustrated using a multivariate probit data example. Supplemental materials for this article (appendix, data, and R code) are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHJlc291cmNlIHhtbG5zPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCIgeG1sbnM6eHNpPSJodHRwOi8vd3d3LnczLm9yZy8yMDAxL1hNTFNjaGVtYS1pbnN0YW5jZSIgeHNpOnNjaGVtYUxvY2F0aW9uPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCBodHRwOi8vc2NoZW1hLmRhdGFjaXRlLm9yZy9tZXRhL2tlcm5lbC00LjEvbWV0YWRhdGEueHNkIj4KICA8aWRlbnRpZmllciBpZGVudGlmaWVyVHlwZT0iRE9JIj4xMC42MDg0L005LkZJR1NIQVJFLjEyMDk2OTYuVjM8L2lkZW50aWZpZXI+CiAgPGNyZWF0b3JzPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5KLiBULiBHYXNraW5zPC9jcmVhdG9yTmFtZT4KICAgIDwvY3JlYXRvcj4KICAgIDxjcmVhdG9yPgogICAgICA8Y3JlYXRvck5hbWU+TS4gSi4gRGFuaWVsczwvY3JlYXRvck5hbWU+CiAgICA8L2NyZWF0b3I+CiAgICA8Y3JlYXRvcj4KICAgICAgPGNyZWF0b3JOYW1lPkIuIEguIE1hcmN1czwvY3JlYXRvck5hbWU+CiAgICA8L2NyZWF0b3I+CiAgPC9jcmVhdG9ycz4KICA8dGl0bGVzPgogICAgPHRpdGxlPlNwYXJzaXR5IEluZHVjaW5nIFByaW9yIERpc3RyaWJ1dGlvbnMgZm9yIENvcnJlbGF0aW9uIE1hdHJpY2VzIG9mIExvbmdpdHVkaW5hbCBEYXRhPC90aXRsZT4KICA8L3RpdGxlcz4KICA8ZGVzY3JpcHRpb25zPgogICAgPGRlc2NyaXB0aW9uIGRlc2NyaXB0aW9uVHlwZT0iQWJzdHJhY3QiPiZsdDtkaXYmZ3Q7Jmx0O3AmZ3Q7Rm9yIGxvbmdpdHVkaW5hbCBkYXRhLCB0aGUgbW9kZWxpbmcgb2YgYSBjb3JyZWxhdGlvbiBtYXRyaXggJmx0O2ImZ3Q74oCJUiZsdDsvYiZndDsgY2FuIGJlIGEgZGlmZmljdWx0IHN0YXRpc3RpY2FsIHRhc2sgZHVlIHRvIGJvdGggdGhlIHBvc2l0aXZlIGRlZmluaXRlIGFuZCB0aGUgdW5pdCBkaWFnb25hbCBjb25zdHJhaW50cy4gQmVjYXVzZSB0aGUgbnVtYmVyIG9mIHBhcmFtZXRlcnMgaW5jcmVhc2VzIHF1YWRyYXRpY2FsbHkgaW4gdGhlIGRpbWVuc2lvbiwgaXQgaXMgb2Z0ZW4gdXNlZnVsIHRvIGNvbnNpZGVyIGEgc3BhcnNlIHBhcmFtZXRlcml6YXRpb24uIFdlIGludHJvZHVjZSBhIHBhaXIgb2YgcHJpb3IgZGlzdHJpYnV0aW9ucyBvbiB0aGUgc2V0IG9mIGNvcnJlbGF0aW9uIG1hdHJpY2VzIGZvciBsb25naXR1ZGluYWwgZGF0YSB0aHJvdWdoIHRoZSBwYXJ0aWFsIGF1dG9jb3JyZWxhdGlvbnMgKFBBQ3MpLCB3aGljaCB2YXJ5IGluZGVwZW5kZW50bHkgb3ZlciAo4oiSMSwxKS4gVGhlIGZpcnN0IHByaW9yIHNocmlua3MgZWFjaCBvZiB0aGUgUEFDcyB0b3dhcmQgemVybyB3aXRoIGluY3JlYXNpbmdseSBhZ2dyZXNzaXZlIHNocmlua2FnZSBpbiBsYWcuIFRoZSBzZWNvbmQgcHJpb3IgKGEgc2VsZWN0aW9uIHByaW9yKSBpcyBhIG1peHR1cmUgb2YgYSB6ZXJvIHBvaW50IG1hc3MgYW5kIGEgY29udGludW91cyBjb21wb25lbnQgZm9yIGVhY2ggUEFDLCBhbGxvd2luZyBmb3IgYSBzcGFyc2UgcmVwcmVzZW50YXRpb24uIFRoZSBzdHJ1Y3R1cmUgaW1wbGllZCB1bmRlciBvdXIgcHJpb3JzIGlzIHJlYWRpbHkgaW50ZXJwcmV0YWJsZSBmb3IgdGltZS1vcmRlcmVkIHJlc3BvbnNlcyBiZWNhdXNlIGVhY2ggemVybyBQQUMgaW1wbGllcyBhIGNvbmRpdGlvbmFsIGluZGVwZW5kZW5jZSByZWxhdGlvbnNoaXAgaW4gdGhlIGRpc3RyaWJ1dGlvbiBvZiB0aGUgZGF0YS4gU2VsZWN0aW9uIHByaW9ycyBvbiB0aGUgUEFDcyBwcm92aWRlIGEgY29tcHV0YXRpb25hbGx5IGF0dHJhY3RpdmUgYWx0ZXJuYXRpdmUgdG8gc2VsZWN0aW9uIG9uIHRoZSBlbGVtZW50cyBvZiAmbHQ7YiZndDvigIlSJmx0Oy9iJmd0OyBvciAmbHQ7YiZndDvigIlSJmx0Oy9iJmd0OyZsdDtzdXAmZ3Q74oiSIDEmbHQ7L3N1cCZndDsgZm9yIG9yZGVyZWQgZGF0YS4gVGhlc2UgcHJpb3JzIGFsbG93IGZvciBkYXRhLWRlcGVuZGVudCBzaHJpbmthZ2Uvc2VsZWN0aW9uIHVuZGVyIGFuIGludHVpdGl2ZSBwYXJhbWV0ZXJpemF0aW9uIGluIGFuIHVuY29uc3RyYWluZWQgc2V0dGluZy4gVGhlIHByb3Bvc2VkIHByaW9ycyBhcmUgY29tcGFyZWQgdG8gc3RhbmRhcmQgbWV0aG9kcyB0aHJvdWdoIGEgc2ltdWxhdGlvbiBzdHVkeSBhbmQgaWxsdXN0cmF0ZWQgdXNpbmcgYSBtdWx0aXZhcmlhdGUgcHJvYml0IGRhdGEgZXhhbXBsZS4gU3VwcGxlbWVudGFsIG1hdGVyaWFscyBmb3IgdGhpcyBhcnRpY2xlIChhcHBlbmRpeCwgZGF0YSwgYW5kIFIgY29kZSkgYXJlIGF2YWlsYWJsZSBvbmxpbmUuJmx0Oy9wJmd0OyZsdDsvZGl2Jmd0OzwvZGVzY3JpcHRpb24+CiAgPC9kZXNjcmlwdGlvbnM+CiAgPHN1YmplY3RzPgogICAgPHN1YmplY3Q+U2NpZW5jZSBQb2xpY3k8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5Jbm9yZ2FuaWMgQ2hlbWlzdHJ5PC9zdWJqZWN0PgogICAgPHN1YmplY3Q+TWF0aGVtYXRpY3M8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5CaW9sb2dpY2FsIFNjaWVuY2VzPC9zdWJqZWN0PgogICAgPHN1YmplY3Q+RXZvbHV0aW9uYXJ5IEJpb2xvZ3k8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5HZW5ldGljczwvc3ViamVjdD4KICA8L3N1YmplY3RzPgogIDxwdWJsaXNoZXI+VGF5bG9yICZhbXA7IEZyYW5jaXM8L3B1Ymxpc2hlcj4KICA8cHVibGljYXRpb25ZZWFyPjIwMTQ8L3B1YmxpY2F0aW9uWWVhcj4KICA8ZGF0ZXM+CiAgICA8ZGF0ZSBkYXRlVHlwZT0iQ3JlYXRlZCI+MjAxNC0xMS0xMTwvZGF0ZT4KICAgIDxkYXRlIGRhdGVUeXBlPSJVcGRhdGVkIj4yMDE2LTAxLTE5PC9kYXRlPgogIDwvZGF0ZXM+CiAgPHJlc291cmNlVHlwZSByZXNvdXJjZVR5cGVHZW5lcmFsPSJEYXRhc2V0Ij5EYXRhc2V0PC9yZXNvdXJjZVR5cGU+CiAgPHNpemVzPgogICAgPHNpemU+MjEyMzUzIEJ5dGVzPC9zaXplPgogIDwvc2l6ZXM+CiAgPHJlbGF0ZWRJZGVudGlmaWVycz4KICAgIDxyZWxhdGVkSWRlbnRpZmllciByZWxhdGVkSWRlbnRpZmllclR5cGU9IkRPSSIgcmVsYXRpb25UeXBlPSJJc1N1cHBsZW1lbnRUbyI+MTAuMTA4MC8xMDYxODYwMC4yMDEzLjg1MjU1MzwvcmVsYXRlZElkZW50aWZpZXI+CiAgICA8cmVsYXRlZElkZW50aWZpZXIgcmVsYXRlZElkZW50aWZpZXJUeXBlPSJET0kiIHJlbGF0aW9uVHlwZT0iSXNJZGVudGljYWxUbyI+MTAuNjA4NC9tOS5maWdzaGFyZS4xMjA5Njk2PC9yZWxhdGVkSWRlbnRpZmllcj4KICA8L3JlbGF0ZWRJZGVudGlmaWVycz4KICA8cmlnaHRzTGlzdD4KICAgIDxyaWdodHMgcmlnaHRzVVJJPSJodHRwczovL2NyZWF0aXZlY29tbW9ucy5vcmcvbGljZW5zZXMvYnkvNC4wLyI+Q0MgQlkgNC4wPC9yaWdodHM+CiAgPC9yaWdodHNMaXN0Pgo8L3Jlc291cmNlPg==","url":"https://tandf.figshare.com/articles/dataset/Sparsity_Inducing_Prior_Distributions_for_Correlation_Matrices_of_Longitudinal_Data/1209696/3","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":15,"viewsOverTime":[{"yearMonth":"2025-09","total":7},{"yearMonth":"2025-10","to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