A Regularized Spatial Market Segmentation Method with Dirichlet Process Gaussian Mixture Prior
Spatially referenced data are increasingly available thanks to the development of modern GPS technology. They also provide rich opportunities for spatial analytics in the field of marketing science. Our main interest is to propose a new efficient statistical framework to conduct spatial segmentation analysis for restaurants located in a metropolitan area in the U.S. The spatial segmentation problem poses important statistical challenges: selecting the optimal number of underlying structures of market segments, capturing complex and flexible spatial structures, and resolving any possible small n and large p issue which can be typical in latent class analysis. Existing approaches try to tackle these issues in heuristic ways or seem silent on them. To overcome these challenges, we propose a new statistical framework based on regularized Bayesian spatial mixture regressions with Dirichlet process integrating ridge or lasso regularization. Our simulation study demonstrates that the proposed models successfully recover the underlying spatial clustering structures and outperforms two existing benchmark models. In the empirical analysis using online customer satisfaction data from the Yelp, our models provides interesting insights on segment-level key drivers of customer satisfaction and interpretable relationships between regional demographics and restaurants' characteristics.