Abstract
Today’s consumer goods markets are rapidly evolving with significant growth in the number of information media as well as the number of competitive products. In this environment, obtaining a quantitative grasp of heterogeneous interactions of firms and customers, which have attracted interest of management scientists and economists, requires the analysis of extremely high-dimensional data. Existing approaches in quantitative research could not handle such data without any reliable prior knowledge nor strong assumptions. Alternatively, we propose a novel method called complex Hilbert principal component analysis (CHPCA) and construct a synchronization network using Hodge decomposition. CHPCA enables us to extract significant comovements with a time lead/delay in the data, and Hodge decomposition is useful for identifying the time-structure of correlations. We apply this method to the Japanese beer market data and reveal comovement of variables related to the consumer choice process across multiple products. Furthermore, we find remarkable customer heterogeneity by calculating the coordinates of each customer in the space derived from the results of CHPCA. Lastly, we discuss the policy and managerial implications, limitations, and further development of the proposed method.
Highlights
In rapidly evolving, highly competitive consumer goods markets, firms are faced with a number of factors affecting business
This plot shows that eigenmodes of complex Hilbert principal component analysis (CHPCA) are more significant in explaining the variation in data than the corresponding eigenmodes in Principal Component analysis (PCA)
The distribution shown in gray is the distribution of the corresponding random rotation simulation (RRS) eigenvalues, whose mean is shown by the short vertical line, and the 2σ range is shown by the horizontal error bars
Summary
Highly competitive consumer goods markets, firms are faced with a number of factors affecting business. These factors often veer away from conventional rules of thumb or theory and can be mutually interacting, providing the challenge of detecting the meaningful relationships between such factors without any strong assumptions. This challenge represents the complexity of consumer choice process caused by the proliferation of viable marketing instruments and competing products. Some consumers might search for information using mobile phones while others might gain detailed
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