Is there a way to utilize Canonical Correlation Analysis when your data are time series and repeated measures (i.e. your experimental units are not independent)? How might one approach the analysis of two sets of variables when the question is what relationships, if any, are there between one set of variables and the other. I was thinking canonical correlation analysis might help me do this, but my variables are count data (not normally distributed) taken over several consecutive years at the same location. In sum, one set of variables is the abundances of various species and the other set is the abundances of a variety of potential food resources.
Perhaps it's best to look at one dependent variable at a time instead of having several dependent variables. Any advice for a statistics novice?
Best Answer
I don't think that using CCA will help you. It appears to me that you have a number of endogenous series ( abundance of species n in number ) and a number of exogenous series ( variety of food resources m in number ). I would suggest constructing n transfer functions each one optimized to fully utilize the information content in the m supporting series and their lags if appropriate while incorporating and unspecified stochastic structure with ARMA and unspecified deterministic structure like Level Shifts/Local Time Trends etc.. Having these n equations unser a "statistical microscope" might illuminate "commonalities" suggesting further grouping of the n equations into subsets.