Confidence intervals for tree-structured varying coefficients

TL;DR

This paper introduces a bootstrap-based method to construct confidence intervals for coefficients in tree-structured varying coefficient models, addressing the uncertainty quantification challenge inherent in data-driven model building.

Contribution

It proposes a novel parametric bootstrap procedure tailored for TSVC models to accurately quantify uncertainty in estimated coefficients.

Findings

The method achieves good coverage properties in simulations.

Application to COVID-19 and infection data demonstrates practical utility.

The approach can be adapted for other tree-based models.

Abstract

The tree-structured varying coefficient model (TSVC) is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, we propose a procedure to construct confidence intervals of the estimated partition-specific coefficients. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, we introduce a parametric bootstrap approach, which is tailored to the complex structure of TSVC. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, we consider applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.