Random intercept selection in structured additive regression models

This paper discusses random intercept selection within the context of semiparametric regression models with structured additive predictor (STAR). STAR models can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. The random intercept selection is based on spike and slab priors for the variances of the random intercept coefficients. The aim is to achieve shrinkage of small random intercept coefficients to zero similar as for the LASSO in frequentist linear models. The mixture structure of the spike and slab prior allows for selective shrinkage, as coefficients are either heavily shrunk under the spike component or left almost unshrunk under the slab component. The hyperparameters of the spike and slab prior are chosen by theoretical considerations based on the prior inclusion probability of a particular random coefficient given the true effect size. Using extensive simulation experiments we compare random intercept models based on spike and slab priors for variances with the usual Inverse Gamma priors. A case study on malnutrition of children in Zambia illustrates the methodology in a real data example.