Inference from the Incomplete Longitudinal Design under an Arma Covariance Structure

JAMES ROCHON. Inference from the Incomplete Longitudinal Design under an ARMA Cdvariance Structure (Under the direction of RONALD W. HELMS). A stochastic model is presented for the analysis of the longitudinal design, appropriate when some of the response variables are missing. The general linear model is used to relate these dependent variables to other variables which are thought to account for inherent variation. An ARMA time series representation is used to model disturbance terms, resulting in a characteristic structure in the covariance matrix among the repeated measures. Maximum likelihood estimation procedures are performed. An unbiased estimator for the general linear model parameter vector is derived, and this estimator is observed to enjoy favourable large-sample properties. There is no convenient expression for the ARMA parameter estimator, and non-linear optimization procedures are prescribed to iterate to a maximizing value. Two broad classes of hypotheses among the indigenous parameters are considered, and procedures to test these hypotheses are derived. The first examines the covariance structure among the repeated measures in an effort to verify the ARMA model. The second considers more substantive hypotheses among the linear model parameters. Two datasets are studied in detail to illustrate the procedures. The first was generated at random from a known stochastic mechanism, while the second was derived from a paper published in the statistical literature. The underlying stochastic patterns are largely verified by the methodology. It is concluded that while the assumptions underpinning the ARMA covariance models may be somewhat restrictive for many practical situations, they nevertheless offer a wide variety of covariance structures, which can have a salutary effect, particularly in the presence of missing values.