In the pricing of customized products, it is challenging to accurately predict the purchase likelihood of potential clients for each personalized request. The heterogeneity of customers and their responses to the personalized products leads to very different purchase behavior. Thus, it is often not appropriate to use a single model to analyze all the pricing data. There is a great need to construct distinctive models for different data segments. In this work, we propose an adaptive convex clustering method to perform data segmentation and model fitting simultaneously for generalized linear models. The proposed method segments data points using the fused penalty to account for the similarity in model structures. It ensures that the data points sharing the same model structure are grouped into the same segment. Accordingly, we develop an efficient algorithm for parameter estimation and study its consistency properties in estimation and clustering. The performance of our approach is evaluated by both numerical examples and case studies of real business data.

In the pricing of customized products, it is challenging to accurately predict the purchase likelihood of potential clients for each personalized request. The heterogeneity of customers and their responses to the personalized products leads to very different purchase behavior. Thus, it is often not appropriate to use a single model to analyze all the pricing data. There is a great need to construct distinctive models for different data segments. In this work, we propose an adaptive convex clustering method to perform data segmentation and model fitting simultaneously for generalized linear models (GLM). The proposed method segments data points using the fused penalty to account for the similarity in model structures. It ensures that the data points sharing the same model structure are grouped into the same segment. Accordingly, we develop an efficient algorithm for parameter estimation and study its consistency properties in estimation and clustering. The performance of our approach is evaluated by both numerical examples and case studies of real business data. Supplementary materials that include all the technical details, proofs, and Python codes used in the article are available online.

In the pricing of customized products, it is challenging to accurately predict the purchase likelihood of potential clients for each personalized request. The heterogeneity of customers and their responses to the personalized products leads to very different purchase behavior. Thus, it is often not appropriate to use a single model to analyze all the pricing data. There is a great need to construct distinctive models for different data segments. In this work, we propose an adaptive convex clustering method to perform data segmentation and model fitting simultaneously for generalized linear models. The proposed method segments data points using the fused penalty to account for the similarity in model structures. It ensures that the data points sharing the same model structure are grouped into the same segment. Accordingly, we develop an efficient algorithm for parameter estimation and study its consistency properties in estimation and clustering. The performance of our approach is evaluated by both numerical examples and case studies of real business data.

The mixture-of-mixtures experiment is different from the classical mixture experiment in that the mixture component in mixture-of-mixtures experiments, known as the major component, is made up of sub-components, known as the minor components. In this paper, we propose an additive heredity model for analyzing mixture-of-mixtures experiments. The proposed model considers an additive structure to inherently connect the major components with the minor components. To enable a meaningful interpretation for the estimated model, the hierarchical and heredity principles are applied by using the nonnegative garrote technique for model selection. The performance of the additive heredity model was compared to several conventional methods in both unconstrained and constrained mixture-of-mixtures experiments. The additive heredity model was then successfully applied in two real-world problems studied previously in the literature.

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