Prior Predictive Check

What is this about?

A prior often feels harmless on the parameter scale — but what does it mean for the data your model considers plausible? The Prior Predictive Check answers exactly that: datasets are simulated from the priors alone (without any real measurements) and shown, e.g., as regression lines or densities. That way you see before the actual fit whether your prior produces realistic or absurd worlds.

Important — upload your own predictors. Whether a prior is plausible depends on the values of your predictors: with β = 2, x = 1 and x = 100 are completely different worlds. Without an upload the tool therefore works with default values — x ~ Normal(0, 1), i.e. z-standardised predictors (50 pseudo-observations per draw). If your predictors are in other units (age in years, income in euros, …), the check is then misleading. With your file (sidebar "Data upload") the tool plugs your real x values into every observation — just like brms does in pp_check. Your y does not feed into the priors; it only appears as a green comparison curve.

How to proceed

1. Choose a model (left) — likelihood family matching your outcome variable; alternatively, build the complete model in the brms Model Builder and transfer it here with one click
2. Upload your own data — CSV with a column y and your predictors as x (or x1, x2, …); optionally group for groups (random effects). That way the check uses your real data structure instead of default values
3. Set priors — via the sidebar, optionally with "⬡ Prior Lab light" as a calculation/visualization aid (CI solver) on the side — you then enter the values you find into the sidebar yourself
4. Look at the simulated data — plausible, or already unrealistic? If the green curve of your real data lies within the range of the blue prior curves, the prior fits the order of magnitude of your data

For a more extensive version of "Prior Lab light" (more distribution types, GLM mode for logit/log link), use the standalone Prior Lab.

Practical extras

⊞ A/B Comparison puts two prior sets side by side; ⊕ Mixed Model adds random effects. A finished model from the brms Model Builder can be transferred directly here (button "⬡ → Builder" for the reverse direction) — R code, SVG and PNG can be exported at any time.

Model

ℹ No Builder import

Prior Presets

Gelman Presets — for z-standardized variables

ℹ When do these presets apply?

Gelman's recommendation Normal(0,2.5) for α and Normal(0,1) for β applies only with z-standardized predictors AND z-standardized DV. For centered (but not divided by SD) predictors: 0 is the mean, but coefficient scaling depends on the raw scale — the prior σ must be adjusted accordingly (roughly: Normal(0, 1) × SD_x × SD_y).

Why? With z-standardized variables, all predictors have SD=1, the DV has SD=1, and coefficients are in SD units — Normal(0,1) for β is a reasonably wide but not unbounded prior.

With raw scales (e.g., income in $, reaction time in ms, blood pressure mmHg), both the σ parameters and the μ of the intercept must be adapted to the actual metric. Example: DV = reaction time (M ≈ 400ms, SD ≈ 80ms) → Prior for α: Normal(400, 100), Prior for β scaled per SD unit of the predictor accordingly.

Rule of thumb: Priors should imply that effects on the DV scale are plausible — the pp_check shows you whether that is the case.

Intercept α

Family

μ (Location) ?Prior mean for α
Expected outcome when x=0 (with z-std.: grand mean).
Depends directly on the DV metric!
Blood pressure: ~120, RT in ms: ~400. 0.0

σ (Scale) ?Prior spread for α
σ=2.5: weakly informative (z-std).
Raw scale: approx. 2–3× the expected SD of the DV. 2.5

Scale μ ± σ max

Predictors β

Interaction terms β

Enter interaction (e.g. x1:x2) + Enter. Each term gets its own β prior (Normal).

Residual spread σ

σ ~ Predictors (distributional)

Prior family ?Prior for σ
Must be positive → positive distributions.
Exponential(1): E[σ]=1.
Half-Normal(1): somewhat wider.

λ (Rate) ?Rate λ (Exponential)
Exponential(1): E[σ]=1.
Exponential(0.5): E[σ]=2.
Kleines λ = flacherer Prior. 1.0

Min Max

Aux-Parameter

Distribution-specific parameters. Priors based on brms recommendations.
Distributional models for these parameters are configurable below.

Simulation

Prior Draws200

pp_check Lines60

Data upload (recommended)

📂 Drop CSV or click
Columns: y, x (or x1, x2 …); group → nGroups auto

∫

Configure priors and run simulation

ℹ Prior Traffic Light — How does it work?

Principle: From each prior draw (α, β, σ), y at x = 0 is computed and sampled. These N values form the prior predictive distribution at the reference point.
🔴 Red — impossible values
· Gamma/Poisson/NegBin/Lognormal: > 2% of y values negative → link does not match α prior
· Poisson/NegBin: Median y > 1,000 → log link explodes (α prior too large)
· Beta/ZI-Beta: > 2% of values outside [0, 1]
· General: > 5% with |y| > 10,000 → priors far too vague
🟡 Yellow — plausible, but check
· Linear: 99%-PI width > 200 → very wide implied outcome scale
· Width < 0.005 → prior extremely tight, little room for data to learn
🟢 Green — plausible
· None of the above criteria apply
· 80%-PI shown: this is how wide the prior uncertainty for y at x = 0 is

      Important: The traffic light checks formal plausibility, not substantive correctness. Green means: the implied y values are in the correct range. Whether the uncertainty is appropriate for your research question is shown by the regression curves and the pp_check below.
    

ℹ Prior Predictive Check

Workflow

1 · Choose model — Likelihood in the dropdown above
2 · Open Prior Lab — explore distributions, find μ/σ
3 · Set priors — preset as starting point, then adjust
4 · Run simulation → traffic light green?
5 · Upload data → pp_check with real x values
6 · Copy brms code → use directly in R. The code sets sample_prior = "only", so it simulates purely from the prior (not the posterior)

What do the plots show?

Regression curves — Prior uncertainty over the linear predictor; each line = one prior draw
Outcome KDE — Which y values does the prior allow? Should roughly cover the range of real data
Marginal KDEs (α, β, σ) — Directly which parameter values the prior permits
KDE = smoothed density estimate; may go slightly below 0 for σ/τ (edge effect) — the draws themselves are always > 0

Multiple predictors & polynomials

Each regression curve varies one predictor — all others are held at 0
x = 0 should be a meaningful reference value — easiest via centering (scale(x, scale=FALSE)): 0 = sample mean, coefficients stay on original scale. Z-standardization (scale()) is optional.
With raw scales (e.g., age in years): set μ ± and σ max in the scale field to the real value range — the x-axis adjusts automatically
Polynomials: degree dropdown per predictor → I(x²), I(x³) are automatically added as separate β terms with separate priors. The regression curve shows the combined curve β₁·x + β₂·x² + …

Mixed Models (LMM)

ICC = τ₀²/(τ₀²+σ²) — proportion of variance due to group differences
ρ = correlation intercept–slope, from LKJ prior

⬡ → Builder: Transfers all priors directly to the brms Model Builder — no copy-paste, no reworking. Reverse: click ⬡ → PP-Check in the Builder. Polynomial terms are fully transferred.