dc.contributor.author	Beaghen, Michael Jr.	en
dc.contributor.committeechair	Smith, Eric P.	en
dc.contributor.committeemember	Arnold, Jesse C.	en
dc.contributor.committeemember	Foutz, Robert	en
dc.contributor.committeemember	Jensen, Donald R.	en
dc.contributor.committeemember	Ye, Keying	en
dc.contributor.department	Statistics	en
dc.date.accessioned	2014-03-14T20:19:29Z	en
dc.date.adate	1997-12-11	en
dc.date.available	2014-03-14T20:19:29Z	en
dc.date.issued	1997-11-13	en
dc.date.rdate	1998-12-11	en
dc.date.sdate	1997-11-13	en
dc.description.abstract	Canonical 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.degree	Ph. D.	en
dc.identifier.other	etd-11997-212717	en
dc.identifier.sourceurl	http://scholar.lib.vt.edu/theses/available/etd-11997-212717/	en
dc.identifier.uri	http://hdl.handle.net/10919/29840	en
dc.publisher	Virginia Tech	en
dc.relation.haspart	etd.pdf	en
dc.relation.haspart	chone.PDF	en
dc.relation.haspart	chtwo.PDF	en
dc.relation.haspart	chthree.PDF	en
dc.relation.haspart	chfour.PDF	en
dc.relation.haspart	chfive.PDF	en
dc.relation.haspart	chsix.PDF	en
dc.relation.haspart	chseven.PDF	en
dc.relation.haspart	cheight.PDF	en
dc.relation.haspart	chnine.PDF	en
dc.relation.haspart	chten.PDF	en
dc.relation.haspart	biblio.PDF	en
dc.relation.haspart	Apone.PDF	en
dc.relation.haspart	Aptwo.PDF	en
dc.relation.haspart	Apthree.PDF	en
dc.relation.haspart	Apfour.PDF	en
dc.relation.haspart	Apfive.PDF	en
dc.relation.haspart	Apsix.PDF	en
dc.relation.haspart	Apseven.PDF	en
dc.relation.haspart	Apeight.PDF	en
dc.relation.haspart	vita.pdf	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	Common Principal Components	en
dc.subject	Procrustes Rotation	en
dc.subject	Redundancy Analysis	en
dc.title	Canonical Variate Analysis and Related Methods with Longitudinal Data	en
dc.type	Dissertation	en
thesis.degree.discipline	Statistics	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	doctoral	en
thesis.degree.name	Ph. D.	en

Canonical Variate Analysis and Related Methods with Longitudinal Data

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