Common principal components analysis (CPCA) of covariance matrices among waterfowl species for plasma-based indices of immune function.

The table shows Flury's Decomposition of Chi Square using step-up and model building approaches [24], [25]. In the step-up approach at each step in the hierarchy the hypothesis labeled “higher” is tested against the hypothesis on the step below, “lower”. The hierarchy is built in a step-wise fashion starting with no relation between the matrices (Unrelated) and rising to CPC(1), then CPC(2), etc, through CPC, Proportionality, and Equality. The likelihood that a particular model is valid is given by the P-value, thus low P-values indicate a low probability that the higher model is better than the lower model [25]. The best solution can also be evaluated using the model building approach where the best model is indicated as the “higher” model in the row with the lowest Akaike information criterion (AIC). Both methods indicate that the matrices share all PCs in common but have different eignevalues (CPC).