  Consider a population consisting of clusters of sampling units, evolving
temporally, spatially, or according to other dynamics. We wish to monitor the
evolution of its means, medians, or other parameters. For administrative
convenience and informativeness, clustered data are often collected via a
rotating plan. Under rotating plans, the observations in the same clusters are
correlated, and observations on the same unit collected on different occasions
are also correlated. Ignoring this correlation structure may lead to invalid
inference procedures. Accommodating cluster structure in parametric models is
difficult or will have a high level of misspecification risk. In this paper, we
explore exchangeability in clustered data collected via a rotating sampling
plan to develop a permutation scheme for testing various hypotheses of
interest. We also introduce a semiparametric density ratio model to facilitate
the multiple population structure in rotating sampling plans. The combination
ensures the validity of the inference methods while extracting maximum
information from the sampling plan. A simulation study indicates that the
proposed tests firmly control the type I error whether or not the data are
clustered. The use of the density ratio model improves the power of the tests.
