Hierarchical Marketing Mix Models with Sign Constraints

TL;DR

This paper introduces a hierarchical marketing mix model that estimates all parameters simultaneously with sign constraints, capturing complex effects of marketing activities, and demonstrates its effectiveness on real data.

Contribution

It proposes a novel simultaneous estimation method for hierarchical MMMs with sign restrictions, improving over multi-stage approaches.

Findings

Effective parameter estimation on real datasets

Captures hierarchical, carryover, shape, and scale effects

Enforces sign constraints aligned with business logic

Abstract

Marketing mix models (MMMs) are statistical models for measuring the effectiveness of various marketing activities such as promotion, media advertisement, etc. In this research, we propose a comprehensive marketing mix model that captures the hierarchical structure and the carryover, shape and scale effects of certain marketing activities, as well as sign restrictions on certain coefficients that are consistent with common business sense. In contrast to commonly adopted approaches in practice, which estimate parameters in a multi-stage process, the proposed approach estimates all the unknown parameters/coefficients simultaneously using a constrained maximum likelihood approach and solved with the Hamiltonian Monte Carlo algorithm. We present results on real datasets to illustrate the use of the proposed solution algorithm.