| Data (multivariate data) on two sets of vectors commonly occur in applications. Statistical analysis of these data is usually done using a canonical correlation analysis (CCA). Occurrence of these data at multiple occasions or conditions leads to longitudinal multivariate data for a CCA. We address the problem of canonical correlation analysis on longitudinal data when the data have a Kronecker product covariance structure. Using structured correlation matrices we model the dependency of repeatedly observed data. Recent work of Srivastava, Nahtman, and von Rosen (2008) developed an iterative algorithm to determine the maximum likelihood estimate of the Kronecker product covariance structure for one set of variables. We implement and generalize their method to estimate the covariance parameters in the context of canonical correlation analysis. We implemented unstructured and autoregressive covariance structures for the repeated measures. However, the developed methods can be easily implemented for other covariance structure. Testing of hypothesis problems using the likelihood ratio test statistics are explored. Bootstrap methods are adopted for calculating the p-values of the tests. Methods are illustrated on a data set obtained from NASA. Performance of the tests is explored using simulation experiments. Consequences of assuming the independence, between repeated measures and performing CCA at different time components, on the distribution of estimated canonical correlations is also explored. Certain simple tests to study the effect of repeated measures are provided here as well. |
