Canonical Analysis

Canonical analysis is the counterpart of simple correlation analysis. In simple correlation two things increase jointly, decrease jointly, or one increases as the other decreases. Whatever they do, they stay in step with each other. Canonical correlation works the same way. The difference is that in canonical correlation sets of variables are correlated with each other instead of individual items. Many pairs of correlates may exist among the different variables. The intent is to find the set with maximum linear correlation. The canonical variates are derived in essentially the same manner as principal components. In PCA the intent is to account for as much of the variance as possible within one set. In canonical correlation, the intent is to account for the maximum amount of correlation between sets. The analysis process searches out the first canonical variate from the first set and the first from the second set that are maximally correlated with each other. It then does the same for the second set and all that follow. Like simple correlation, the two first correlates may be plotted against each other; so too may the second set, and any others that exist. Like PCA, only the first few correlates may be of interest. Correlation may be between sets of sensory measurements, sets of instrumental measurements, or more commonly between sensory and instrumental measurements. Canonical analysis has some similarity to MRA. In MRA the dependent variable is singular whereas the independent variables are multiple; in canonical correlation, both sets are multiple.

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