Testing For Homogeneity Of Variances And Correlation In Longitudinal Models With Uniform Correlation And Exponential Correlation

Analysis of longitudinal data is a hot topic in recent years, and is an important method to investigate statistical characteristic displayed in the data, which is measured repeatedly over time or space for each study participant. It is necessary to make a reasonable covariance structure for longitudinal data so as to fit these data with linear or nonlinear models. The likely sources modelling covariance structure of longitudinal data include random effects, serial correlation and measurement errors. Diggle et al(1994), Wolfinger(1995) proposed covariance structures of uniform correlation and exponential correlation, and it is necessary to test for the rationality of these assumptions. This thesis studies the tests for homogeneity of variances and correlation coefficients in longitudinal data models with uniform correlation and exponential correlation.Chapter 2 studies the tests for heteroscedasticity and correlation in longitudinal data model with uniform correlation covariance structure. Firstly we consider the tests for uniform correlation and homogeneity of uniform correlation coefficients while variance is homogeneous; then we discuss the tests for homogeneity of variance while uniform correlation coefficients is homogeneous, and the combined tests for homogeneity of variance and uniform correlation coefficients; finally we study the combined tests for correlation and homogeneity of variance. Some test statistics are obtained, these tests are illustrated with an example and Monte Carlo simulations.Chapter 3 investigates the tests for heteroscedasticity and correlation in longitudinal data model with exponential correlation covariance structure. The covariance structures are different when the observation times are equally spaced or irregularly spaced, so we divide it into two way to discuss. Firstly we discuss the tests for heteroscedasticity and correlation in longitudinal data model with exponential correlation at the case of equally spaced, and then the other. Finally these tests are illustrated with examples.In summary, we have thoroughly and systematically studied the tests for homogeneity of variances and correlation coefficients in longitudinal data model with two correlation structure. A series of new test statistics are obtained, and illustrative examples and Monte Carlo simulations show that the test techniques are very well.