  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.
