Selective inference for additive and linear mixed models

After model selection, subsequent inference in statistical models tends to be overconfident if selection is not accounted for. One possible solution to address this problem is selective inference, which constitutes a post-selection inference framework and yields valid inference statements by conditioning on the selection event. Existing work on selective inference is, however, not directly applicable to additive and linear mixed models. A novel extension to recent work on selective inference to the class of additive and linear mixed models is thus presented. The approach can be applied for any type of model selection mechanism that can be expressed as a function of the outcome variable (and potentially of covariates on which the model conditions). Properties of the method are validated in simulation studies and in an application to a data set in monetary economics. The approach is particularly useful in cases of non-standard selection procedures, as present in the motivating application.