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dc.contributor.authorBeaghen, Michael Jr.en_US
dc.date.accessioned2014-03-14T20:19:29Z
dc.date.available2014-03-14T20:19:29Z
dc.date.issued1997-11-13en_US
dc.identifier.otheretd-11997-212717en_US
dc.identifier.urihttp://hdl.handle.net/10919/29840
dc.description.abstractCanonical variate analysis (CVA) is a widely used method for analyzing group structure in multivariate data. It is mathematically equivalent to a one-way multivariate analysis of variance and often goes by the name of canonical discriminant analysis. Change over time is a central feature of many phenomena of interest to researchers. This dissertation extends CVA to longitudinal data. It develops models whose purpose is to determine what is changing and what is not changing in the group structure. Three approaches are taken: a maximum likelihood approach, a least squares approach, and a covariance structure analysis approach. All methods have in common that they hypothesize canonical variates which are stable over time. The maximum likelihood approach models the positions of the group means in the subspace of the canonical variates. It also requires modeling the structure of the within-groups covariance matrix, which is assumed to be constant or proportional over time. In addition to hypothesizing stable variates over time, one can also hypothesize canonical variates that change over time. Hypothesis tests and confidence intervals are developed. The least squares methods are exploratory. They are based on three-mode PCA methods such as the Tucker2 and parallel factor analysis. Graphical methods are developed to display the relationships between the variables over time. Stable variates over time imply a particular structure for the between-groups covariance matrix. This structure is modeled using covariance structure analysis, which is available in the SAS package Proc Calis. Methods related to CVA are also discussed. First, the least squares methods are extended to canonical correlation analysis, redundancy analysis, Procrustes rotation and correspondence analysis with longitudinal data. These least squares methods lend themselves equally well to data from multiple datasets. Lastly, a least squares method for the common principal components model is developed.en_US
dc.publisherVirginia Techen_US
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dc.rightsI hereby grant to Virginia Tech or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.en_US
dc.subjectCommon Principal Componentsen_US
dc.subjectProcrustes Rotationen_US
dc.subjectRedundancy Analysisen_US
dc.titleCanonical Variate Analysis and Related Methods with Longitudinal Dataen_US
dc.typeDissertationen_US
dc.contributor.departmentStatisticsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineStatisticsen_US
dc.contributor.committeechairSmith, Eric P.en_US
dc.contributor.committeememberArnold, Jesse C.en_US
dc.contributor.committeememberFoutz, Roberten_US
dc.contributor.committeememberJensen, Donald R.en_US
dc.contributor.committeememberYe, Keyingen_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-11997-212717/en_US
dc.date.sdate1997-11-13en_US
dc.date.rdate1998-12-11
dc.date.adate1997-12-11en_US


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