Prior Predictive Check

Model

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

Simulation

Prior Draws200

pp_check Lines60

Data upload (optional)

📂 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

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 to ensure via z-standardization (0 = mean, ±1 = one SD)
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.

Model

Prior Presets

Intercept α

Predictors β

Interaction terms β

Residual spread σ

ν Degrees of freedom (Student-t)

Aux-Parameter

Random Effects (LMM)

Simulation

Data upload (optional)

Prior Predictive Check

Model

Prior Presets

Intercept α

Predictors β

Interaction terms β

Residual spread σ

ν Degrees of freedom (Student-t)

Aux-Parameter

Random Effects (LMM)

Simulation

Data upload (optional)

Prior Lab