HIERARCHICAL BAYESIAN MODELING OF LATENT RANKING PROCESSES

Abstract

This paper proposes a universal Bayesian hierarchical model for estimating latent ranking processes in e-commerce search engines. Unlike traditional regression approaches, ranking is considered as an ordinal manifestation of an unobserved rating, the dynamics of which are described by a random walk with price drift. The model combines an equation of state, an ordinal logistic model of observations, and hierarchical pooling of sensitivity across product categories. The architecture is invariant to the platform and the structure of the algorithm’s features. The proposed approach allows for the time dependence of observations to be taken into account and the latent state of the system to be reconstructed without access to internal ranking mechanisms, significantly expanding the capabilities of quantitative analysis of digital platform search algorithms. The estimation is performed entirely in a Bayesian setting using the MCMC (NUTS) method, obtaining posterior distributions of the parameters and hidden states of change. Empirical verification was conducted on a proprietary panel sample of search results generated by the monitoring system. The obtained results confirm the effectiveness of the model for reconstructing hidden rankings, identifying heterogeneity in price sensitivity between categories, and predicting position changes without access to the ranking algorithm.