“Estimating Distributional Models With Brms: Additive Distributional Models”, Paul Bürkner2019-08-29 (R, Bayes; similar)⁠:

This vignette provides an introduction on how to fit distributional regression models with brms. We use the term distributional model to refer to a model, in which we can specify predictor terms for all parameters of the assumed response distribution.

In the vast majority of regression model implementations, only the location parameter (usually the mean) of the response distribution depends on the predictors and corresponding regression parameters. Other parameters (eg. scale or shape parameters) are estimated as auxiliary parameters assuming them to be constant across observations. This assumption is so common that most researchers applying regression models are often (in my experience) not aware of the possibility of relaxing it. This is understandable insofar as relaxing this assumption drastically increase model complexity and thus makes models hard to fit. Fortunately, brms uses Stan on the backend, which is an incredibly flexible and powerful tool for estimating Bayesian models so that model complexity is much less of an issue.

…In the examples so far, we did not have multilevel data and thus did not fully use the capabilities of the distributional regression framework of brms. In the example presented below, we will not only show how to deal with multilevel data in distributional models, but also how to incorporate smooth terms (ie. splines) into the model. In many applications, we have no or only a very vague idea how the relationship between a predictor and the response looks like. A very flexible approach to tackle this problems is to use splines and let them figure out the form of the relationship.

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