Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently....

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion, <sc>aic</sc>, have been used, based either on the marginal or on the conditional distribution. We show that the marginal <sc>aic</sc> is not an asymptotically unbiased...