  We propose a novel spike and slab prior specification with scaled beta prime
marginals for the importance parameters of regression coefficients to allow for
general effect selection within the class of structured additive distributional
regression. This enables us to model effects on all distributional parameters
for arbitrary parametric distributions, and to consider various effect types
such as non-linear or spatial effects as well as hierarchical regression
structures. Our spike and slab prior relies on a parameter expansion that
separates blocks of regression coefficients into overall scalar importance
parameters and vectors of standardised coefficients. Hence, we can work with a
scalar quantity for effect selection instead of a possibly high-dimensional
effect vector, which yields improved shrinkage and sampling performance
compared to the classical normal-inverse-gamma prior. We investigate the
propriety of the posterior, show that the prior yields desirable shrinkage
properties, propose a way of eliciting prior parameters and provide efficient
Markov Chain Monte Carlo sampling. Using both simulated and three large-scale
data sets, we show that our approach is applicable for data with a potentially
large number of covariates, multilevel predictors accounting for hierarchically
nested data and non-standard response distributions, such as bivariate normal
or zero-inflated Poisson.
