Confidence intervals for tree-structured varying coefficients

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.