Redundancy Analysis

The interrelationships between two sets of measurements made on the same subjects can be studied by canonical correlation. Originally developed by Hotelling, the canonical correlation is the maximum correlation between linear functions or canonical factors of two sets of variables. An alternative pair of statistics to investigate the interrelationships between two sets of variables are the redundancy indices, developed by Stewart and Love. A redundancy coefficient is an index of the average proportion of variance in the variables in one set that is reproducible from the variables in the other set. Unlike canonical correlation, redundancy indices are non-symmetric in that a measure can be calculated for each set of variables (predictor and criterion) and need not be equal to each other. Van Den Wollenberg has developed a method of extracting factors that maximize redundancy, as opposed to canonical correlation. DeSarbo, Johansson, and Israels have developed extensions of this methodology. Takane and Hwang developed extended redundancy analysis to generalize redundancy analysis to investigate asymmetric or directional associations among more than two sets of variables, analogous to the work of Carroll and Kettenring regarding generalized canonical correlation analysis. A sports marketing application is provided examining the relationship between the different ways consumers/fans follow their college football team and their various attitudes, opinions, and lifestyles (i.e., psychographics) regarding sports