Efficient subgroup testing in change-plane models

TL;DR

This paper introduces a new weighted average score test for detecting change planes in regression models, improving power especially with many grouping variables, and extends it to GEE and multiple change planes.

Contribution

A novel weighted average score test (WAST) for change-plane detection that outperforms classic tests and extends to GEE and multiple change planes.

Findings

WAST significantly improves test power in large grouping variable scenarios.

Asymptotic distributions of WAST are derived under null and alternative hypotheses.

Bootstrap method effectively approximates critical values for WAST.

Abstract

Considered here is a hypothesis test for the coefficients in the change-plane regression models to detect the existence of a change plane. The test that is considered is from the class of test problems in which some parameters are not identifiable under the null hypothesis. The classic exponential average tests do not work well in practice. To overcome this drawback, a novel test statistic is proposed by taking the weighted average of the squared score test statistic (WAST) over the grouping parameter's space, which has a closed form from the perspective of the conjugate priors when an appropriate weight is chosen. The WAST significantly improves the power in practice, particularly in cases where the number of the grouping variables is large. The asymptotic distributions of the WAST are derived under the null and alternative hypotheses. The approximation of critical value by the bootstrap method is investigated, which is theoretically guaranteed. Furthermore, the proposed test method is naturally extended to the generalized estimating equation (GEE) framework, as well as multiple change planes that can test if there are three or more subgroups. The WAST performs well in simulation studies, and its performance is further validated by applying it to real datasets.