Effects of Multi-Brand, Multi-Channel Usage on Consumers' Purchase Decisions and Amounts: A Bayesian Hierarchical Sample Selection Model Incorporating Individual Heterogeneity*,**

Purpose: As digitalization and channel diversification reshape retail landscapes, consumers increasingly interact with multiple brands across online and offline platforms in dynamic, non-linear purchasing journeys. This complexity challenges the traditional CRM paradigm, which often overlooks the effects of competing brands and channels. Prior omni-channel research typically assumes a closed-system view, focusing on internal brand-channel integration, yet real-world environments are open and asymmetric. Crucially, consumer decision-making involves two structurally distinct stages—whether to purchase and how much to spend—each governed by different behavioral drivers, which are often conflated in existing models. Moreover, each individual exhibits unique patterns of multi-channel behavior, requiring analysis at the individual level. To address these realities, this study develops a competitive multi-channel interaction framework that captures dual decision structures, cross-brand engagement, and individual heterogeneity to explain acquisition, loyalty, and churn in competitive retail settings. Research design, data, and methodology: We employ a 105-week unbalanced panel dataset integrating credit card transactions, mobile app usage patterns, and offline store visit logs, providing a multidimensional view of actual consumer behavior across digital and physical retail contexts. The sample comprises 445 consumers with persistent multi-brand engagement, supporting high-resolution analysis of channel interactions. To jointly estimate purchase incidence and conditional purchase amount while correcting for selection bias, we apply a Bayesian Hierarchical Sample Selection Model. This framework accommodates individual-level heterogeneity in channel responsiveness and captures the asymmetric behavioral influence of focal versus competitor brand engagement. Demographic covariates are integrated to model variation in behavioral sensitivity across consumer segments. This approach enables both theoretical insights into dual-stage decision logic and practical applications in targeted marketing, customer life cycle management, and channel optimization. Results: Our findings reveal a pronounced asymmetry in the behavioral determinants of purchase decisions. Competitor channel usage—especially via online platforms—significantly reduces the probability of focal brand purchase, underscoring its predictive value as a churn indicator. However, competitor engagement has no discernible effect on spending among those who do purchase. Notably, simultaneous use of our brand’s offline channel and competitor B’s online channel increases purchase incidence, suggesting latent cross-channel complementarities. In contrast, purchase amounts are positively influenced only by focal brand engagement, particularly in-store dwell time. The model further uncovers contrasting demographic effects: female, older, and unmarried consumers exhibit lower purchase likelihoods, while higher spending is associated with being female, unmarried, and having higher income. These divergent effects between purchase incidence and amount reinforce the importance of separating acquisition from monetization strategies and emphasize the need for fine-grained, behaviorally informed customer segmentation. Conclusions: This research introduces and empirically validates a competitive multi-brand, multi-channel interaction theory, advancing the literature beyond conventional mono-brand omni-channel models by capturing how consumer engagement with competing channels shapes decision-making in open-market contexts. Rather than focusing exclusively on internal integration, we demonstrate the strategic relevance of competitor channel monitoring for early churn detection and customer acquisition. While methodologically robust, our framework serves a broader managerial purpose: it separates purchase behavior into incidence and amount, each with distinct behavioral antecedents and targeting implications. This dual-structure perspective, coupled with consumer-level heterogeneity, provides a scalable foundation for ROI-driven channel investment, predictive churn analytics, and micro-targeted marketing in competitive, data-rich retail environments.