Selective Inference for Additive and Linear Mixed Models

TL;DR

This paper develops a selective inference framework for additive and linear mixed models, enabling valid post-model selection inference even with complex or non-standard selection procedures.

Contribution

It extends recent selective inference methods to additive and linear mixed models, accommodating various model selection mechanisms based on outcome and covariates.

Findings

Simulation studies confirm valid inference post-selection.

Application to monetary economics data demonstrates practical utility.

Framework handles non-standard and hierarchical model selection procedures.

Abstract

This work addresses the problem of conducting valid inference for additive and linear mixed models after model selection. One possible solution to overcome overconfident inference results after model selection is selective inference, which constitutes a post-selection inference framework, yielding valid inference statements by conditioning on the selection event. We extend recent work on selective inference to the class of additive and linear mixed models for any type of model selection mechanism that can be expressed as a function of the outcome variable (and potentially on covariates on which it conditions). We investigate the properties of our proposal in simulation studies and apply the framework to a data set in monetary economics. Due to the generality of our proposed approach, the presented approach also works for non-standard selection procedures, which we demonstrate in our application. Here, the final additive mixed model is selected using a hierarchical selection procedure, which is based on the conditional Akaike information criterion and involves varying data set sizes.