Hypothesis Testing In The Longitudinal Data Model

Longitudinal data is referred to data in which individuals are measured repeatedly through time, so it combines elements of cross-sectional data and time-series data.The prominent advantage of longitudinal data is that it can analyze effectively the change of individuals over time. However, it is complicated by repeated measurement within individuals and variation among individuals. In Diggle et al (2002), parametric models for covariance structure are built according to the likely sources modeling covariance structure of longitudinal data: random effects, serial correla-tion(specially AR(1)) and measurement errors. Just based on parametric models for covariance structure, estimating covariance parameters by means of REML estimation, this paper studies the hypothesis tests of mean parameters and covariance parameters in the longitudinal linear models.The parametric models of covariance structure clearly describes the resources of heteroscedasticity in longitudinal data. On the other hand, it brings about parsimonious covariance structure. Thus, estimation for covariance parameters is more effective. REML estimation as a method of estimating covariance parameters is more effective than ML estimation when the number of regression parameters is large and covariance matrix is near-singular. Furthermore, it can detach covariance parameters from regression parameters. Therefore, covariance parameters are only considered when test statistics are derived, which simplifies problems.This paper includes two main parts. Part one is hypothesis testing of regression parameters. As a result of the complexity of covariance structure, test problems are studied under several widely used types of covariance structure, and F test statistics, likelihood test statistics, Wald test statistics and Score test statistics are derived. The other part is hypothesis testing of covariance parameters. Reasonable choice of covariance structure can improve the efficiency of mean structure and provide better estimates of estimated parameters, so selecting qualitatively reasonable covariance structure by means of hypothesis test is quite meaningful. In this part, testhypothesis is built according to the parametric models of covariance structure and Scare test statistics is obtained. In every part, one practical data set is presented to illustrate the application of these methods.