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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,

This work focuses on the study and development of a model for longitudinal data which accommodates irregularly-timed, inconsistently-timed, and randomly-missing data while taking into account the correlation between observations on the same individual with an AR(l) type of covariance structure. This model will be referred to as the model with generalized AR(l) covariance or as the model with exponentially decreasing correlation. Standard methods of analysis for these types of data, such as the General Linear Multivariate Model, require assuming that the data are consistently-timed between individuals. Further, observations with missing data would need to be discarded in order to use such a model. Another useful model for this type of data is the General Linear Model with ARMA covariance structure, as described by Rochon (1989). However, this model does not allow for unequally-spaced observations within individuals, although missing observations can be accommodated. Maximum Likelihood and Restricted Maximum Likelihood Estimators are derived for the parameters of the model with exponentially decreasing correlation and