/faq/index.html This section collects longer-form answers to recurring MMM, Bayesian, and panel-econometrics questions that come up when practitioners move from classical econometrics to PanelMMM. The pages are written for technical readers who already understand regression, panel data, and causal inference, but want the Abacus framing. Core model concepts Adstock and Saturation for Econometricians — Why modern MMM uses carryover and diminishing-returns transformations instead of log-linear shortcuts. Causal Identification in Marketing Mix Modelling — What an MMM can and cannot identify causally from observational data. HSGP (Hilbert Space Gaussian Process) for Econometricians — How flexible time-varying effects map to familiar basis and shrinkage ideas. Baseline vs Media Trade-Offs in MMM — Why baseline terms and media terms can trade attribution against each other even when fit quality looks similar. Priors and model checking Bayesian Priors for Econometricians — How priors relate to constraints, penalties, and regularisation you already use in classical work. Prior Predictive Checks for Econometricians — How to test whether your configured priors imply plausible behaviour before fitting. Posterior Predictive Checks for Econometricians — How to judge whether the fitted model reproduces the data well enough to trust downstream interpretation. Computation and comparison MCMC Diagnostics for Econometricians — How to read trace plots, R-hat, ESS, and divergences. Model Comparison for Econometricians — How to think about ELPD, LOO-CV, posterior predictive checks, and their limitations. Panel specification Do We Need a Mundlak Specification Test in Abacus? — Why Abacus uses posterior inspection of CRE terms rather than a frequentist Mundlak test. Suggested reading order If you are new to Bayesian MMM, a practical sequence is: Hugo en-gb /faq/bayesian_priors_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/bayesian_priors_for_econometricians/index.html This document addresses common concerns that econometricians have about Bayesian priors, reframes them using familiar econometric concepts, and discusses the practical trade-offs between “tight” and “loose” prior specifications in the context of Marketing Mix Modeling. 1. Are priors subjective? Don’t they bias the results? This is the most common objection from econometricians. The short answer is: you are already using priors, you just call them something else. /faq/adstock_saturation_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/adstock_saturation_for_econometricians/index.html In classical econometrics, you model diminishing returns by taking the logarithm of spend: $\log(\text{spend})$ enters the regression, and the coefficient captures an elasticity. Carryover effects, if considered at all, are handled with lagged dependent variables or Koyck distributed lags. These approaches are simple and familiar. They are also, for media measurement, inadequate. This document explains the two non-linear transformations at the heart of every modern Marketing Mix Model — adstock (carryover) and saturation (diminishing returns) — and shows why they are more flexible, more interpretable, and more economically grounded than the classical alternatives. We also address a subtle but important modelling decision: whether to apply adstock before saturation, or saturation before adstock. /faq/hsgp_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/hsgp_for_econometricians/index.html This document answers common questions econometricians may have when encountering HSGP (Hilbert Space Gaussian Process) approximations in the codebase, particularly regarding model flexibility and the number of basis functions. 1. Does a Hilbert Space Gaussian Process use up degrees of freedom when modelling? Yes, but not in the strict $N - k$ counting sense used in classical OLS econometrics. Instead, Gaussian Processes (and their HSGP approximations) use “effective degrees of freedom” (EDF) due to Bayesian regularization. /faq/mcmc_diagnostics_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/mcmc_diagnostics_for_econometricians/index.html If you have spent your career reading Stata output — coefficient tables, standard errors, t-statistics, p-values, and the occasional Durbin-Watson statistic — then your first encounter with MCMC output will feel disorienting. There are no p-values. There is no single “estimate.” Instead, there are thousands of draws from something called a posterior distribution, accompanied by diagnostics you have never seen: R-hat, ESS, divergences, trace plots. This document maps every one of these concepts back to something you already understand, so you can read Bayesian output with the same confidence you bring to a regression table. /faq/prior_predictive_checks_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/prior_predictive_checks_for_econometricians/index.html If you come from classical econometrics, you are used to checking assumptions after estimation: residual plots, heteroskedasticity tests, outlier influence, and maybe out-of-sample fit. Bayesian workflow adds one earlier question: Before fitting anything, do my priors imply plausible behaviour for the target variable? That is what prior predictive checking answers. 1. Why parameter-level priors are not enough A prior can look sensible when you inspect it in isolation and still imply absurd behaviour once it flows through the whole model. /faq/posterior_predictive_checks_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/posterior_predictive_checks_for_econometricians/index.html Posterior predictive checking asks a simple question: After fitting the model, can it reproduce the main features of the observed data? For a classically trained econometrician, this is the Bayesian analogue of residual diagnostics, fitted-versus-observed checks, and out-of-sample sanity-checking, but with one important difference: the checks are based on the full posterior distribution, not a single point estimate. 1. What the check actually is After fitting, you sample from the posterior predictive distribution: /faq/model_comparison_for_econometricians/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/model_comparison_for_econometricians/index.html You have spent your career comparing models with AIC, BIC, adjusted $R^2$, and the occasional likelihood ratio test. These tools are elegant, fast, and deeply embedded in econometric practice. They are also, in the Bayesian setting, either inapplicable or subtly misleading. This document explains the Bayesian model comparison toolkit — LOO-CV, ELPD, posterior predictive checks — by mapping each concept back to something you already understand. We also discuss the pitfalls that arise when comparing ELPD across models, because this is where even experienced practitioners make mistakes. /faq/causal_identification_in_mmm/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/causal_identification_in_mmm/index.html If you are a classically trained econometrician, you have every right to be sceptical of Marketing Mix Models. The causal identification strategy underpinning MMM is weaker than the methods you were taught to trust. This document confronts that reality head-on: we explain what MMM can and cannot claim causally, where the identifying assumptions break down, and how modern calibration techniques partially rescue the framework. We also place MMM on the “causal ladder” relative to the gold-standard methods you already know. /faq/baseline_vs_media_tradeoffs_in_mmm/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/baseline_vs_media_tradeoffs_in_mmm/index.html One of the most confusing experiences in MMM is this: two specifications can fit the target series almost equally well both can have acceptable diagnostics yet they can assign very different amounts of the target to media versus baseline This is not necessarily a bug in the software. It is a structural feature of the problem. This page explains how that trade-off appears in Abacus and why you should expect it. /faq/mundlak_specification_test/index.html Mon, 01 Jan 0001 00:00:00 +0000 /faq/mundlak_specification_test/index.html Background Classical panel econometrics uses the Mundlak specification test (also called the Chamberlain–Mundlak test) to decide whether random effects (RE) or fixed effects (FE) should be preferred. Stata 19 implements this as estat mundlak — a Wald test on the auxiliary Mundlak γ coefficients: H₀: RE is consistent (γ = 0 jointly), so the simpler RE model is adequate. H₁: RE is inconsistent (γ ≠ 0), so CRE or FE is needed. This test is the cluster-robust-compatible replacement for the classical Hausman test, which breaks under heteroskedasticity or within-cluster correlation.