  Mixture-of-Experts models are commonly used when there exist distinct
clusters with different relationships between the independent and dependent
variables. Fitting such models for large datasets, however, is computationally
virtually impossible. An attractive alternative is to use a subdata selected by
``maximizing" the Fisher information matrix. A major challenge is that no
closed-form expression for the Fisher information matrix is available for such
models. Focusing on clusterwise linear regression models, a subclass of MoE
models, we develop a framework that overcomes this challenge. We prove that the
proposed subdata selection approach is asymptotically optimal, i.e., no other
method is statistically more efficient than the proposed one when the full data
size is large.
