  Statistical modelling strategy is the key for success in data analysis. The
trade-off between flexibility and parsimony plays a vital role in statistical
modelling. In clustered data analysis, in order to account for the
heterogeneity between the clusters, certain flexibility is necessary in the
modelling, yet parsimony is also needed to guard against the complexity and
account for the homogeneity among the clusters. In this paper, we propose a
flexible and parsimonious modelling strategy for clustered data analysis. The
strategy strikes a nice balance between flexibility and parsimony, and accounts
for both heterogeneity and homogeneity well among the clusters, which often
come with strong practical meanings. In fact, its usefulness has gone beyond
clustered data analysis, it also sheds promising lights on transfer learning.
An estimation procedure is developed for the unknowns in the resulting model,
and asymptotic properties of the estimators are established. Intensive
simulation studies are conducted to demonstrate how well the proposed methods
work, and a real data analysis is also presented to illustrate how to apply the
modelling strategy and associated estimation procedure to answer some real
problems arising from real life.
