Linear Models for Multivariate Repeated Measures Data

<p>In this dissertation we focus mainly on the analysis of continuous multivariate repeated measurements data based on the assumption of multivariate normality. However certain aspects of the analysis of univariate repeated measures data are also considered. Typically, we have measurements on p variables (possibly correlated) in the form of px1 vectors y_ijk observed at k = 1,2, ...,t_ij occasions on j = 1,2, ..., n_i individuals from i = 1,2, ..., g groups. We assume a naturally occurring covariance structure V_ij ⊗ ∑ among the p variables on the j^th individual from i^th group made at t_ij occasions. Here V_ij and ∑ are positive definite matrices of order t_ij x t_ij and p x p respectively. We develop a general linear model approach to accommodate both balanced and unbalanced repeated measures data.</p> <p>Our main results are: (1) construction of Rao's score test for a simpler model with p=1 (univariate case) and V_ij having a structure as in a mixed effects model, (2) comparison of all the methods for analyzing univariate repeated measures data with time varying covariates, (3) derivation of the maximum likelihood estimates of the covariance matrices<strong> V</strong> and <strong>∑ </strong> in the balanced case, (4) derivation of Satterthwaite type approximation to the distribution of multivariate quadratic forms, (5) estimation of degrees of freedom for these approximations, and (6) derivation of the maximum likelihood estimates of the covariance parameters under certain specific covariance structures for unbalanced case.</p> <p>Rao's score test is derived in Chapter 2. Analysis of repeated measures in the presence of time varying covariates is a useful but difficult problem. In Chapter 3, we review the existing methods for analyzing repeated measured data with time varying covariates and discuss their computational aspects using SAS software. We also point out that a linear model approach yields a unified tool to analyze these data. In Chapter 4, various results about balanced multivariate repeated measures models are derived. We present the entire scheme of analysis of balanced multivariate data including the computational details. Finally, the analysis of unbalanced multivariate repeated measures is discussed in Chapter 5. In this case we assume two commonly used covariance structures namely equicorrelation and autoregressive structures for V_ij and derive the maximum likelihood estimates of the unknown parameters.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

1996

Author dc:creator

• Rao, Shantha S.

Contributors dc:contributor

• Dayanand N. Naik
• Narasinga R. Chaganty
• John P. Morgan
• Ardythe L. Morrow

• Linear models
• Multivariate
• Data
• Statistics and Probability

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Repository record dc:identifier

https://digitalcommons.odu.edu/mathstat_etds/47

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1050