  We propose a multi-threshold change plane regression model which naturally
partitions the observed subjects into subgroups with different covariate
effects. The underlying grouping variable is a linear function of covariates
and thus multiple thresholds form parallel change planes in the covariate
space. We contribute a novel 2-stage approach to estimate the number of
subgroups, the location of thresholds and all other regression parameters. In
the first stage we adopt a group selection principle to consistently identify
the number of subgroups, while in the second stage change point locations and
model parameter estimates are refined by a penalized induced smoothing
technique. Our procedure allows sparse solutions for relatively moderate- or
high-dimensional covariates. We further establish the asymptotic properties of
our proposed estimators under appropriate technical conditions. We evaluate the
performance of the proposed methods by simulation studies and provide
illustration using two medical data. Our proposal for subgroup identification
may lead to an immediate application in personalized medicine.
