Marketing Mix Modeling
A Study of Confounding and Experimental Calibration

Independent Research - University of Tennessee
Bayesian MMM, Causal Inference, PyMC-Marketing, Synthetic Data

Independent Research · Associated with Haslam College of Business · University of Tennessee, Knoxville · USA

Can We Trust Marketing ROI?

A synthetic-data study testing whether observational Marketing Mix Modeling can recover true causal ROI, and what it takes to make it trustworthy when it can't.

Independent Research Causal Inference Bayesian Modeling
PyMC-Marketing Bayesian MMM (NUTS) Python Causal DAGs Geo-Lift Test Calibration Meta Robyn Dataset

Supervisor: Dr. Russell Zaretzki (Heath Faculty Fellow, Business Analytics & Statistics; Haslam College of Business, University of Tennessee, Knoxville, USA)

Additional Resources: Paper (Document) · Git Repository

Marketing Mix Modeling (MMM) is widely used to allocate media budgets, but it relies on observational data; leaving it vulnerable to confounding from organic demand, ad-targeting mechanisms, and macroeconomic trends. Measuring the true return on ad spend is a notoriously hard problem (Lewis & Rao, 2015): randomized lift tests isolate the causal effect cleanly but are too expensive and slow to run continuously (Gordon et al., 2019), while MMM evaluates all channels at once from historical data but faces well-documented identification challenges of its own (Chan & Perry, 2017). This project asks a direct question: can an observational MMM be trusted to recover causal ROI, and if not, what does it actually take to make it trustworthy?

I don't propose new estimation methodology here. The Bayesian MMM builds on classic market-response modeling (Hanssens et al., 2001) and Bayesian media-mix formulations with adstock and saturation effects (Jin et al., 2017); the backdoor-adjustment framework follows standard causal-DAG theory (Neuberg, 2003) (Hernán & Robins, 2020); and the calibration-via-prior technique follows Zhang et al.'s approach to combining MMM with experimental lift tests (Zhang et al., 2024). The contribution is empirical: using synthetic data with known ground truth, I show concretely when these established methods succeed, when they fail, and what it takes to correct them, then validate the same failure pattern on a real, public dataset.

Research Questions

Three questions, one synthetic dataset

Because the ground-truth ROI is known by construction in synthetic data, estimation accuracy and bias can be measured directly rather than assumed.

01

Recovery

When the truth is known, do the model's posteriors actually cover the true ROI?

02

Confounding

How much does omitting a demand confounder bias ROI, and does adjusting for it fix the bias?

03

Calibration

Can an experimental lift estimate, injected as a prior, correct an MMM that observational data alone gets wrong?

Methodology

A four-stage experimental design

Every stage keeps the same Bayesian model, priors, adstock, saturation, seasonality, and sampler settings; so differences in results come from the data and controls, not from changing the model.

01

Parameter Recovery

Fit a naive OLS, an oracle OLS with known transforms, and a full Bayesian MMM on clean synthetic data where spend is assigned independently of demand; the best-case scenario for any observational method.

02

Confounding & Backdoor Adjustment

Introduce a latent demand confounder that drives both spend and revenue. Fit the same model with the confounder uncontrolled (backdoor open) and controlled (backdoor closed), then compare.

03

Experimental Calibration

Simulate a randomized geo-lift test (Sun et al., 2017) on one channel and inject its ROI estimate as an informative prior, following Zhang et al.'s calibration approach (Zhang et al., 2024); while leaving the demand confounder unmeasured and the backdoor open.

04

Real-World Validation

Refit the Bayesian MMM on Meta's public Robyn dataset (208 weeks, five channels), with and without a competitor-sales control, to check whether the synthetic failure pattern replicates on real data.

Model & Tools

Built with

PyMC-Marketing v0.19.3 Bayesian NUTS Sampler Geometric Adstock Hill Saturation Fourier Seasonality DAG-Based Backdoor Adjustment Geo-Lift Test Simulation Synthetic Data Generation Meta Robyn Dataset Python
Key Results

What each stage found

Four stages, from the best-case scenario to a real, uncontrolled dataset.

Stage 1 — Recovery

Can a Bayesian MMM recover true ROI with no confounding at all?

Media spend was assigned independently of demand, so the backdoor path doesn't exist; the most favorable setting possible for an observational method.

Solution

Yes. Every channel's true ROI fell inside the model's 95% credible interval, with 94.2% of weeks inside the 90% predictive interval (predictive R² = 0.91). But low-spend channels like Email and Display carried very wide intervals: accurate coverage, low precision.

Stage 2 — Confounding

How much does an unmeasured demand confounder distort ROI, and does adjustment fix it?

A latent demand signal was wired into both spend and revenue, opening a backdoor path. The model was fit with and without a control for it.

Solution

Search's ROI was overestimated by +2.74 with the backdoor open, dropping to +0.97 once adjusted, adjustment worked well here. Email was worse (+7.99 → +5.72) despite the weakest demand link; its bias was mostly pre-existing model weakness, not confounding, so adjustment alone couldn't fix it.

Stage 3 — Calibration

Without an observable confounder to adjust for, can one experiment still correct the model?

A simulated geo-lift test on Search (ROI = 3.9 ± 0.4) was injected as an informative prior, with the demand confounder left unmeasured and the backdoor open the entire time.

Solution

Search's median ROI shrank from 6.57 (naive) to 4.35 (calibrated), with the credible interval tightening to [3.37, 5.36]. The fix was channel-specific though; Email, left uncalibrated, stayed inflated at 11.66.

Stage 4 — Real-World Validation

Does the same confounding pattern show up outside synthetic data?

The Bayesian MMM was refit on Meta's public Robyn dataset (208 weeks, five channels), once with a competitor-sales control and once without it.

Solution

Dropping the confounder inflated Search ROI by +73.3% and Facebook by +32.6%, while upper-funnel channels like TV and Print moved the opposite direction; the exact signature seen in the synthetic experiment, confirmed without ever knowing the real ground truth.

Navigating real-world deployment requires a unified approach: combining observational MMM with randomized lift testing to get causally robust ROI estimates. Neither approach alone is enough; observational data is scalable but confounded, and experiments are unbiased but too expensive to run for every channel.

Gallery

Figures

References

2024

  1. Media mix model calibration with Bayesian priors
    Yingxiang Zhang, Mike Wurm, Eddie Li, Alexander Wakim, Joseph Kelly, Brenda Price, and Ying Liu
    2024

2020

  1. Causal Inference: What If Chapman & Hall
    MA Hernán and JM Robins
    CRC, Boca Raton, 2020

2019

  1. A comparison of approaches to advertising measurement: Evidence from big field experiments at Facebook
    Brett R Gordon, Florian Zettelmeyer, Neha Bhargava, and Dan Chapsky
    Marketing Science, 2019

2017

  1. Challenges and opportunities in media mix modeling
    David Chan and Michael Perry
    Google Inc, 2017
  2. Bayesian methods for media mix modeling with carryover and shape effects
    Yuxue Jin, Yueqing Wang, Yunting Sun, David Chan, and Jim Koehler
    Google Research, 2017
  3. Geo-level bayesian hierarchical media mix modeling
    Yunting Sun, Yueqing Wang, Yuxue Jin, David Chan, and Jim Koehler
    URL: https://ai. google/research/pubs/pub46000, 2017

2015

  1. The unfavorable economics of measuring the returns to advertising
    Randall A Lewis and Justin M Rao
    The Quarterly Journal of Economics, 2015

2003

  1. Causality: models, reasoning, and inference, by judea pearl, cambridge university press, 2000
    Leland Gerson Neuberg
    Econometric Theory, 2003

2001

  1. Market response models: Econometric and time series analysis
    Dominique M Hanssens, Leonard J Parsons, and Randall L Schultz
    2001