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Model-based small area estimation is frequently used in conjunction withsurvey data in order to establish estimates for under-sampled or unsampledgeographies. These models can be specified at either the area-level, or theunit-level, but unit-level models often offer potential advantages such as moreprecise estimates and easy spatial aggregation. Nevertheless, relative toarea-level models, literature on unit-level models is less prevalent. Inmodeling small areas at the unit level, challenges often arise as a consequenceof the informative sampling mechanism used to collect the survey data. Thispaper provides a comprehensive methodological review for unit-level modelsunder informative sampling, with an emphasis on Bayesian approaches. To provideinsight into the differences between methods, we conduct a simulation studythat compares several of the described approaches. In addition, the methodsused for simulation are further illustrated through an application to theAmerican Community Survey. Finally, we present several extensions and areas forfuture research.

Unit Level Modeling of Survey Data for Small Area Estimation Under Informative Sampling: A Comprehensive Overview with Extensions