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Then, in basic linear regression, we specify a predictor term \(\eta_\) to reflect that \(\sigma\) constitutes a standard deviation and thus only takes on positive values, while a linear predictor can be any real number.Īnother important application of the distributional regression framework are so called zero-inflated models. Suppose we have a normally distributed response variable. 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. This is understandable insofar as relaxing this assumption drastically increase model complexity and thus makes models hard to fit. This assumption is so common that most researchers applying regression models are often (in my experience) not aware of the possibility of relaxing it.
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Other parameters (e.g., scale or shape parameters) are estimated as auxiliary parameters assuming them to be constant across observations. 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. 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.
#NONMEM 3 NEW RESIDUAL VARIABILITY MODELS ETA ON SIGMA HOW TO#
This vignette provides an introduction on how to fit distributional regression models with brms.