Index: Zhang Vaver 2017 - Aggregate Marketing System Simulator

Zhang Vaver 2017 - Aggregate Marketing System Simulator

Routing Summary

This folder fully captures Zhang & Vaver (2017), Introduction to the Aggregate Marketing System Simulator (AMSS). AMSS is a hidden-state Markov simulator of aggregate marketing time series, with counterfactual ground truth for ROAS and mROAS. The folder has 10 notes: an overview with a complete source map, motivation, the segmentation and migration formalism, natural migration and lag, two media modules, the sales event, ground truth, the MMM evaluation study, and discussion.

• Need the big picture or a section → note map? → Zhang Vaver 2017 - Aggregate Marketing System Simulator - Overview
• Why simulate, and what is a virtual experiment? → AMSS Motivation - Virtual Experiments for Marketing Measurement
• The 198 segments, the event sequence, multinomial migration (Eqs. 1-2)? → AMSS Hidden-State Consumer Segmentation and Migration Formalism
• Seasonality/market rate, de-satiation, how carryover arises (row-identical matrices, $Q_{\alpha }$)? → AMSS Natural Migration, Satiation and Lagged-Effect Mechanics
• TV/radio: reach, frequency, the Hill effect, GRPs? → AMSS Traditional Media Module (Reach, Frequency, Hill Effect)
• Paid search: auction, SOV/CPC, organic vs paid incrementality? → AMSS Paid Search Module (Queries, Auction, Organic vs Paid)
• Demand curves, competitor strength and substitutability, satiation after purchase? → AMSS Sales Event - Demand Curves, Competition and Post-Purchase Migration
• How ground-truth ROAS/mROAS is computed, and which interventions are well defined? → AMSS Ground Truth - Counterfactual Scenarios and Simulated ROAS
• Tables 4-7 and the regression MMM results with and without lag? → AMSS MMM Evaluation - Simple Scenario and Lagged-Effects Study
• Limitations and a protocol for validating an MMM or SHAP pipeline with a simulator? → AMSS Discussion, Limitations and Validation Practice

Concept Map

Concept	Note	Type	Depends On	Key Result
Event sequence / sequential interaction	AMSS Hidden-State Consumer Segmentation and Migration Formalism	definition	—	Each event affects all later ones through the segmentation
198 mindset segments	AMSS Hidden-State Consumer Segmentation and Migration Formalism	definition	—	6 category × 33 brand segments
Multinomial migration law	AMSS Hidden-State Consumer Segmentation and Migration Formalism	definition	—	Eqs. 1-2: $m\sim \text{Mult}(a,q_{s,\cdot })$, $n^{\prime }=n-a+\sum m$
Market-rate targeting	AMSS Natural Migration, Satiation and Lagged-Effect Mechanics	definition	Migration law	$E[r_{t,2}]={\rho }_t$ with minimal migration
No-lag theorem / lag family	AMSS Natural Migration, Satiation and Lagged-Effect Mechanics	theorem	Migration law	No lag iff row-identical; $Q_{\alpha }^{\top }n=(1-\alpha )\Vert n\Vert x+\alpha n$
Hill effect on frequency	AMSS Traditional Media Module (Reach, Frequency, Hill Effect)	definition	Migration law	$H(f)=1/(1+(f/\kappa {)}^{-\zeta })$, EC50 $\kappa$
Reach from Poisson exposures	AMSS Traditional Media Module (Reach, Frequency, Hill Effect)	algorithm	—	Miss probability $\approx e^{-v/a}$; reach $=a^{\ast }-U$, $U\approx N({\mu }_1,{\mu }_2-{\mu }_1^2)$
Search auction (CPC, SOV)	AMSS Paid Search Module (Queries, Auction, Organic vs Paid)	definition	—	$c_t={\eta }^{(m)}\vee c^{\ast }\wedge {\eta }^{(M)}$; linear SOV
Organic vs paid exposure effect	AMSS Paid Search Module (Queries, Auction, Organic vs Paid)	definition	Search auction	$e={\psi }_w(\cdot )+{\psi }_u(\cdot )+{\psi }_v(\cdot )$
Competitor strength/substitutability	AMSS Sales Event - Demand Curves, Competition and Post-Purchase Migration	definition	—	$r^{(z)}=\{\gamma -(1-\omega )r^{(y^{\ast })}\}\vee 0$
Counterfactual types / total effect	AMSS Ground Truth - Counterfactual Scenarios and Simulated ROAS	definition	All modules	Set budgets, not search spend or sales
Simulated ROAS estimator	AMSS Ground Truth - Counterfactual Scenarios and Simulated ROAS	theorem	Counterfactuals	Pairwise-ratio average $\to \theta$ by LLN; mROAS = 5% cut
Lag-omission bias	AMSS MMM Evaluation - Simple Scenario and Lagged-Effects Study	result	Lag family, ROAS	TV-ROAS MSE 0.025 → 1.618 (no-lag model) vs 0.002 → 0.067 (lags)
Simulator validation protocol	AMSS Discussion, Limitations and Validation Practice	algorithm	Ground truth	Freeze pipeline, vary one difficulty, score with MC SEs

Notes

• Zhang Vaver 2017 - Aggregate Marketing System Simulator - Overview — CONTAINS: research question, contribution, key findings, full Source Map (every §, Tables 1-8, Figs. 1-14, Eqs. 1-14), placement in ADEMP, grouped reference list, worked reading of the headline lag result
• AMSS Motivation - Virtual Experiments for Marketing Measurement — CONTAINS: Abstract and §1 argument (limits of experiments, unverifiable assumptions), virtual experiment definition (fn. 1), purpose of a simulated ad system
• AMSS Hidden-State Consumer Segmentation and Migration Formalism — CONTAINS: Fig. 1 event architecture, sequential-interaction principle, Table 1 (six dimensions), Fig. 2, Tables 2-3 (198 segments), purchase-state brand-choice drivers, favorability vs loyalty statements, Eqs. 1-2, App. A notation (Table 8), the l=5/6 index inconsistency
• AMSS Natural Migration, Satiation and Lagged-Effect Mechanics — CONTAINS: market rate and App. B.1 entry/exit matrices (Eq. 10), de-satiation (Eq. 11), natural migration (Eq. 12) and origin restrictions, no-lag theorem (Eq. 13) with proof, $Q_{\alpha }$ lag family (Eq. 14), marketing-actionable dimensions, lag arithmetic example
• AMSS Traditional Media Module (Reach, Frequency, Hill Effect) — CONTAINS: Fig. 3, the six-step algorithm (audience, budget, flighting, gamma unit cost, GRPs, Poisson reach/frequency, effect), Eq. 3 Hill, budget notation and Q4 newspaper example, reach = audience minus unreached with variance mu2 - mu1^2, the beta notation clash, extensibility to new modules, effect-scaled matrix, product construction of the maximal matrix, TV parameterisation of §4 and Fig. 9
• AMSS Paid Search Module (Queries, Auction, Organic vs Paid) — CONTAINS: Fig. 4, the ten-step algorithm (campaign settings, queries, CPC/SOV, binomial impressions, NegBin click cap, hypergeometric clicks, multinomial allocation), App. C.2 max-CPC = bid and the two ways to cut budget, the weekly vs daily cap inconsistency, the chained query/impression/click occupancy draws, exposure-type effect formula, incrementality via zero budget, §4 search parameterisation, Figs. 10-11
• AMSS Sales Event - Demand Curves, Competition and Post-Purchase Migration — CONTAINS: linear demand curves, Fig. 5, competitor strength $\gamma$ and substitutability $\omega$, Fig. 6, multinomial purchase and Poisson units, revenue, profit (named but undefined), post-purchase satiation and brand update, §4 sales settings, worked competition arithmetic
• AMSS Ground Truth - Counterfactual Scenarios and Simulated ROAS — CONTAINS: prediction/attribution/optimization, scenario definition, three counterfactual types, total-effect pathways, ROAS estimator with remarks (ratio of means, total spend), mROAS and base sales, Table 4
• AMSS MMM Evaluation - Simple Scenario and Lagged-Effects Study — CONTAINS: ADEMP mapping, full §4.1.1 parameter table (Eqs. 4-5, Figs. 7-9), Figs. 10-13, Tables 4-7, Model 1 (Eq. 6), Model 2 (Eq. 7), lag manipulation, Fig. 14 bias readings, findings, bias-variance example, Table 5 vs 7 caveat
• AMSS Discussion, Limitations and Validation Practice — CONTAINS: §5 conclusions, table of acknowledged simplifications, critical limitations, simulator-validation protocol, illustrative SHAP-pipeline and Rashomon-check examples

Sources

• Zhang Vaver 2017 - Introduction to the Aggregate Marketing System Simulator — Zhang, S. & Vaver, J. (2017). Introduction to the Aggregate Marketing System Simulator. Google technical report, 13 April 2017, 43 pp.

See Also

• Morris White Crowther 2019 - Simulation Studies (ADEMP) - Overview — how to design and report the simulation study that AMSS feeds
• Chan Perry 2017 - Challenges in Media Mix Modeling - Overview — the companion catalogue of MMM challenges to simulate
• Bayesian Media Mix Modeling - Overview — model-side Hill, adstock and ROAS
• Geo-Experiment Methodology - Overview — experimental methods AMSS can also evaluate
• Dillon et al - SHAP and Causal Insights - Overview — predictive attribution vs causal effect