Title: Effect selection in distributional regression
Authors: Nadja Klein - Georg-August-University Goettingen (Germany)
Thomas Kneib - University of Goettingen (Germany)
Manuel Carlan - University of Goettingen (Germany) [presenting]
Stefan Lang - University of Innsbruck (Germany)
Helga Wagner - Johannes Kepler University (Austria)
Abstract: A spike-and-slab prior specification is proposed that allows us to carry the concept of Bayesian variable selection over to general effect selection within the class of structured additive distributional regression models comprising various effect types such as non-linear effects, varying coefficients, spatial effects, random effects as well as potentially hierarchical regression structures. The spike-and-slab prior is assigned to the prior standard deviation of blocks of regression coefficients which allows us to work with a scalar quantity instead of dealing with possibly high-dimensional effect vectors. Furthermore, we specify the model in a redundant parameterisation with parameter expansion that yields improved shrinkage and sampling performance compared to the classical normal-inverse-gamma prior. We investigate the propriety of the posterior distribution, show that the proposed prior structure yields desirable shrinkage properties, propose an interpretable way of eliciting prior parameters and provide an efficient Markov Monte Carlo sampling scheme. Using both simulated data and three real data sets, we show that our approach is applicable for data with a potentially large number of covariates, multilevel predictor structures accounting for hierarchically nested data and a wide range of non-standard response distributions such as bivariate normal or zero-inflated Poisson with regression effects on all distributional parameters.