  Estimation of heterogeneous treatment effects is an active area of research.
Most of the existing methods, however, focus on estimating the conditional
average treatment effects of a single, binary treatment given a set of
pre-treatment covariates. In this paper, we propose a method to estimate the
heterogeneous causal effects of high-dimensional treatments, which poses unique
challenges in terms of estimation and interpretation. The proposed approach
finds maximally heterogeneous groups and uses a Bayesian mixture of regularized
logistic regressions to identify groups of units who exhibit similar patterns
of treatment effects. By directly modeling group membership with covariates,
the proposed methodology allows one to explore the unit characteristics that
are associated with different patterns of treatment effects. Our motivating
application is conjoint analysis, which is a popular type of survey experiment
in social science and marketing research and is based on a high-dimensional
factorial design. We apply the proposed methodology to the conjoint data, where
survey respondents are asked to select one of two immigrant profiles with
randomly selected attributes. We find that a group of respondents with a
relatively high degree of prejudice appears to discriminate against immigrants
from non-European countries like Iraq. An open-source software package is
available for implementing the proposed methodology.
