An Approximate F Statistic for Testing Population Effects in Longitudinal Studies via Mixed Models

This work focuses on developing and characterizing a statistic for testing contrasts among population effects and developing confidence regions for those effects using data from longitudinal studies. Historically, likelihood ratio or Wald-type statistics were used for such analyses, but those statistics produce very optimistic Type I error rates. McCarroll and Helms (1987) introduced an ad hoc F statistic (FH) with reasonable Type I error rates, but no information was available on distributional properties of that statistic. This research substantially extends McCarroll and Helms' results by characterizing the distributional and numerical properties of an alternative form of FH. Longitudinal studies, which playa key role in medical, epidemiological, and environmental research, are designed to characterize patterns in experimental units' response over some longitudinal metameter and to investigate the effects of covariates on responses. Characteristics of longitudinal data from such research limit traditional univariate and multivariate methods. Often data are mistimed or irregularly timed, and missing observations result in incomplete data. This work establishes procedures that provide hypothesis tests and confidence intervals for such data using the Linear Mixed Model (MixMod). An alternative parameterization of MixMod is developed, and a modified form of the FH statistic is derived. The Helms-McCarroll procedure is used to derive restricted maximum likelihood estimates for the covariance parameters usi~g the concentrated likelihood (Callanan and Harville, 1988) to concentrate the error variance out of the estimating equations. Conditional on these estimates, the