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We provide a flexible framework for selecting among a class of additivepartial linear models that allows both linear and nonlinear additivecomponents. In practice, it is challenging to determine which additivecomponents should be excluded from the model while simultaneously determiningwhether nonzero additive components should be represented as linear ornon-linear components in the final model. In this paper, we propose a Bayesianmodel selection method that is facilitated by a carefully specified class ofmodels, including the choice of a prior distribution and the nonparametricmodel used for the nonlinear additive components. We employ a series of latentvariables that determine the effect of each variable among the threepossibilities (no effect, linear effect, and nonlinear effect) and thatsimultaneously determine the knots of each spline for a suitable penalizationof smooth functions. The use of a pseudo-prior distribution along with acollapsing scheme enables us to deploy well-behaved Markov chain Monte Carlosamplers, both for model selection and for fitting the preferred model. Ourmethod and algorithm are deployed on a suite of numerical studies and areapplied to a nutritional epidemiology study. The numerical results show thatthe proposed methodology outperforms previously available methods in terms ofeffective sample sizes of the Markov chain samplers and the overallmisclassification rates.

Bayesian model selection in additive partial linear models via locally adaptive splines