Likelihood Compass
Data-generating process β†’ distribution family β†’ brms implementation
Β© Dr. Rainer DΓΌsing Β· Interactive Tools by Claude
Likelihood Compass β€” which distribution family fits your data-generating process?  Β·  Not "what does the histogram look like?" β€” but "how did these numbers come to be?"

The choice of distribution family (likelihood function) for your own data can be narrowed down considerably with a few targeted questions and considerations. Different data-generating processes lead to different distributions of the data: reaction times, sum scores from test items, and count data with a heterogeneous rate each produce characteristic shapes that can be predicted before the first observation, if the generating process is known.

Stage 1: Narrow down possible criteria through targeted questions and considerations.
Stage 2: Look at the data and assess how well the distribution fits.
Stage 3: What to watch for in brm(), and which parameters and priors are needed.

Free flexibility: the one-parameter trick
Student-t instead of Normal, Negative Binomial instead of Poisson, Beta-Binomial instead of Binomial: in all three cases the more robust family adds one extra parameter to the standard model. This parameter controls how far the model may deviate from the simpler distribution β€” for instance through outliers or overdispersion. When that extra flexibility isn't needed, the model automatically approaches the standard case (Ξ½ β†’ ∞, Ο† β†’ ∞).
No rigid scheme
The mapping in Stage 1 is a well-reasoned starting hypothesis, not a law. Under certain conditions β€” large n, clean measurement conditions, few outliers, interest in the mean rather than the tails β€” the classical standard (Normal, Poisson, Binomial) remains a legitimate, simpler choice. If several candidates in Stage 2 converge to practically the same result, that is itself an informative answer: the family didn't matter for this particular question.
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Prior Predictive Check
Before looking at real data: simulates datasets purely from distribution family + priors. Does the combination generate plausible values β€” or does it predict impossible magnitudes, negative reaction times, or proportions > 1? A wrong likelihood type often shows up here, before any fitting happens.
πŸ“ˆ
Posterior Predictive Check
After estimation: simulates datasets from the fitted model and compares them directly against the real data. This is where a wrong likelihood becomes most visible β€” the simulations systematically miss the skew, bounds, or spread of the real data.
βš–
LOO Lab β€” Model Comparison
The actual referee: Leave-One-Out cross-validation estimates how well each model predicts unseen data β€” not just how well it traces the training data. Two families that were close together in Stage 2 can be pitted directly against each other here.
β„Ή Likelihood Compass β€” Help
What will I learn here?
This tool helps with a decision that comes up before every regression: which distribution family fits your data. What matters is not just how the data look in a histogram, but what type of data it is and through which process the values came to be. Most people reach for Normal, Poisson, or Binomial distributions automatically β€” not because these families fit best, but because they're the most familiar. A deliberate look at the generating process costs little and prevents an ill-fitting likelihood from silently biasing estimates, standard errors, or predictions.
The three stages
See also β†’ Distribution Lab for every distribution family in detail and brms Model Builder for the finished model code.
Further reading
McElreath (2020) β€” Statistical Rethinking, ch. 10–12 (GLMs & their distribution families)