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Prior Predictive Check

Prior Predictive Checks Β· brms Β· 15 Likelihoods Β· A/B Comparison Β· LMM Β· Builder Integration

Β© Dr. Rainer DΓΌsing Β· Interactive Tools by Claude

Model

Prior Presets

Gelman Presets β€” for z-standardized variables
β„Ή When do these presets apply?
Gelman's recommendation Normal(0,2.5) for Ξ± and Normal(0,1) for Ξ² 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 β€” the prior Οƒ must be adjusted accordingly (roughly: Normal(0, 1) Γ— SD_x Γ— SD_y).

Why? With z-standardized variables, all predictors have SD=1, the DV has SD=1, and coefficients are in SD units β€” Normal(0,1) for Ξ² is a reasonably wide but not unbounded prior.

With raw scales (e.g., income in $, reaction time in ms, blood pressure mmHg), both the Οƒ parameters and the ΞΌ of the intercept must be adapted to the actual metric. Example: DV = reaction time (M β‰ˆ 400ms, SD β‰ˆ 80ms) β†’ Prior for Ξ±: Normal(400, 100), Prior for Ξ² scaled per SD unit of the predictor accordingly.

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

Intercept Ξ±

Family
ΞΌ (Location) ?Prior mean for Ξ±
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
Οƒ (Scale) ?Prior spread for Ξ±
Οƒ=2.5: weakly informative (z-std).
Raw scale: approx. 2–3Γ— the expected SD of the DV. 2.5
Scale ΞΌ Β± Οƒ max

Predictors Ξ²

Interaction terms Ξ²

Enter interaction (e.g. x1:x2) + Enter. Each term gets its own Ξ² prior (Normal).

Residual spread Οƒ

Prior family ?Prior for Οƒ
Must be positive β†’ positive distributions.
Exponential(1): E[Οƒ]=1.
Half-Normal(1): somewhat wider.
Ξ» (Rate) ?Rate Ξ» (Exponential)
Exponential(1): E[Οƒ]=1.
Exponential(0.5): E[Οƒ]=2.
Kleines Ξ» = flacherer Prior. 1.0
Min Max

Simulation

Prior Draws200
pp_check Lines60

Data upload (optional)

πŸ“‚ Drop CSV or click
Columns: y, x (or x1, x2 …); group β†’ nGroups auto
∫
Configure priors and run simulation
← brms Model Builder LOO Lab β†’

Prior Lab

Distribution Explorer Β· Prior Visualizer Β· brms-ready
Distribution
Parameter
GLM Mode
x-axis:
⟳ Prior Credible Interval β†’ Parameters
Specify the desired Prior Credible Interval β€” the solver automatically finds the matching parameters.
Lower bound
Upper bound
Mass (%)
⚠  brms Intercept Prior β€” Note
This tool always uses the explicit 0 + Intercept formulation:
y ~ 0 + Intercept + x

This means the intercept prior set here applies directly on the raw scale β€” without internal centering by brms. The intercept prior describes the expected y-value when all predictors = 0.

Recommendation: Center predictors (scale(x, scale=FALSE)): then x=0 = sample mean, the intercept prior describes the expected y for an average observation β€” and regression coefficients remain directly interpretable on the original scale.
Z-standardization (scale()) is optional and only needed when predictors should be brought to comparable units. β†’ Centering recommended Β· z-standardization optional.
β„Ή Prior Predictive Check
Workflow
What do the plots show?
Multiple predictors & polynomials
Mixed Models (LMM)
⬑ β†’ Builder: Transfers all priors directly to the brms Model Builder β€” no copy-paste, no reworking. Reverse: click ⬑ β†’ PP-Check in the Builder. Polynomial terms are fully transferred.
Further Reading