# Hierarchical Marketing Mix Models with Sign Constraints

arXiv: https://arxiv.org/abs/2008.12802 · HTML: https://mlsanity.com/paper/2008.12802/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [Doubly Robust Counterfactual Classification](https://mlsanity.com/paper/2301.06199/) (2023)
- [CausalMMM: Learning Causal Structure for Marketing Mix Modeling](https://mlsanity.com/paper/2406.16728/) (2024)
- [A new framework for Marketing Mix Modeling: Addressing Channel Influence Bias and Cross-Channel Effects](https://mlsanity.com/paper/2311.05587/) (2023)
- [Hierarchical Clustering As a Novel Solution to the Notorious Multicollinearity Problem in Observational Causal Inference](https://mlsanity.com/paper/2606.30992/) (2026)

## Abstract (arXiv)

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.