  Model-based small area estimation is frequently used in conjunction with
survey data in order to establish estimates for under-sampled or unsampled
geographies. These models can be specified at either the area-level, or the
unit-level, but unit-level models often offer potential advantages such as more
precise estimates and easy spatial aggregation. Nevertheless, relative to
area-level models, literature on unit-level models is less prevalent. In
modeling small areas at the unit level, challenges often arise as a consequence
of the informative sampling mechanism used to collect the survey data. This
paper provides a comprehensive methodological review for unit-level models
under informative sampling, with an emphasis on Bayesian approaches. To provide
insight into the differences between methods, we conduct a simulation study
that compares several of the described approaches. In addition, the methods
used for simulation are further illustrated through an application to the
American Community Survey. Finally, we present several extensions and areas for
future research.
