Analysis of Asymmetric Relationships Among Soft Drink Brands

Abstract

AbstractBrand switching data among eight soft drink brands were analyzed. The data are represented by an 8 × 8 brand switching matrix. The brand switching matrix is inevitably asymmetric, because the relationship from brand j to brand k is not necessarily equal to the relationship from brand k to brand j. The brand switching matrix was analyzed by asymmetric multidimensional scaling based on singular value decomposition. The four-dimensional result was chosen as the solution. The solution gives the outward tendency, which represents the strength of switching from a corresponding brand to the other brands along each dimension, and the inward tendency, which represents the strength of switching to a corresponding brand from the other brands along each dimension. The solution disclosed that the differences between diet and non-diet brands as well as between cola and lemon-lime brands played important roles in the brand switching.KeywordsDiagonal ElementSingular VectorHorizontal DimensionDominance RelationshipFourth QuadrantThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.