Multivariate Repeated Measures Data Research Articles

Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix

In this article we consider a set of t repeated measurements on p variables (or characteristics) on each of the n individuals. Thus, data on each individual is a p 2 t matrix. The n individuals themselves may be divided and randomly assigned to g groups. Analysis of these data using a MANOVA model, assuming that the data on an individual has a covariance matrix which is a Kronecker product of two positive definite matrices, is considered. The well-known Satterthwaite type approximation to the distribution of a quadratic form in normal variables is extended to the distribution of a multivariate quadratic form in multivariate normal variables. The multivariate tests using this approximation are developed for testing the usual hypotheses. Results are illustrated on a data set. A method for analysing unbalanced data is also discussed.

An f-test for multivariate repeated measures data with the wiener stochastic process pattern in the covariance matrix

In the analysis of repeated measures experiments certain patterns may arise in the structure of the covariance matrix.We can take advantage of these patterns when testing the equality of means hypothesis in that the patterned covariance matrix can be reduced to diagonal form.In estimating the parameters of the diagonal matrix, we get more degrees of freedom for our estimates because we have fewer parameters to estimate.This increase in degrees of freedom leads to a more powerful test of the equality of means hypothesis.One such pattern that is reducible to diagonal form is the Wiener Stochastic Process pattern.Assuming this pattern is present in the structure of the covariance matrix, maximum likelihood estimates of the mean and covariance matrices will be derived.Using these estimates, we derive an exact F-test of the equality of means hypothesis.