Canonical Variate Analysis and Related Methods with Longitudinal Data

dc.contributor.authorBeaghen, Michael Jr.en
dc.contributor.committeechairSmith, Eric P.en
dc.contributor.committeememberArnold, Jesse C.en
dc.contributor.committeememberFoutz, Roberten
dc.contributor.committeememberJensen, Donald R.en
dc.contributor.committeememberYe, Keyingen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T20:19:29Zen
dc.date.adate1997-12-11en
dc.date.available2014-03-14T20:19:29Zen
dc.date.issued1997-11-13en
dc.date.rdate1998-12-11en
dc.date.sdate1997-11-13en
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
dc.description.degreePh. D.en
dc.identifier.otheretd-11997-212717en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-11997-212717/en
dc.identifier.urihttp://hdl.handle.net/10919/29840en
dc.publisherVirginia Techen
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dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCommon Principal Componentsen
dc.subjectProcrustes Rotationen
dc.subjectRedundancy Analysisen
dc.titleCanonical Variate Analysis and Related Methods with Longitudinal Dataen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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