Using Canonical Correlation to Construct Product Spaces for Objects with Known Feature Structures
Given a set of attribute ratings of objects with known feature structures, one can construct product spaces by use of various compositional methods. Factor and discriminant analyses are two such well-known compositional approaches. A third, comparatively neglected, procedure involves the use of objects-, features-, or interactions-based canonical correlation analysis (CCA). These three CCA methods are compared and then illustrated by an application to data based on judgmental ratings of sweater designs. The comparative results of the three types of canonical correlation suggest the potential usefulness of CCA methods in deriving spatial representations to explore the nature of attribute judgments, particularly if one wishes to construct product spaces at the individual level of analysis or desires clarification of the judgmental effects of feature interactions.