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Abstract Unit-level modeling strategies offer many advantages relative to the area-level models that are most often used in the context of small area estimation. For example, unit-level models aggregate naturally, allowing for estimates at any desired resolution, and also offer greater precision in many cases. We compare a variety of the methods available in the literature related to unit-level modeling for small area estimation. Specifically, to provide insight into the differences between methods, we conduct a simulation study that compares several of the general approaches. In addition, the methods used for simulation are further illustrated through an application to the American Community Survey.
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A Comprehensive Overview of Unit-Level Modeling of Survey Data for Small Area Estimation Under Informative Sampling
Abstract Model-based small area estimation is frequently used in conjunction with survey data 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 article provides a comprehensive methodological review for unit-level models under informative sampling, with an emphasis on Bayesian approaches.
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- PAR ID:
- 10447837
- Date Published:
- Journal Name:
- Journal of Survey Statistics and Methodology
- ISSN:
- 2325-0984
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Small area estimation (SAE) has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression, where the variance for each domain is assumed to be known and plugged in following a design-based estimate. Recent work has considered hierarchical models for the variance, where the design-based estimates are used as an additional data point to model the latent true variance in each domain. These hierarchical models may incorporate covariate information but can be difficult to sample from in high-dimensional settings. Utilizing recent distribution theory, we explore a class of Bayesian hierarchical models for SAE that smooth both the design-based estimate of the mean and the variance. In addition, we develop a class of unit-level models for heteroscedastic Gaussian response data. Importantly, we incorporate both covariate information as well as spatial dependence, while retaining a conjugate model structure that allows for efficient sampling. We illustrate our methodology through an empirical simulation study as well as an application using data from the American Community Survey.more » « less
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The Household Pulse Survey, recently released by the U.S. Census Bureau, gathers information about the respondents’ experiences regarding employment status, food security, housing, physical and mental health, access to health care, and education disruption. Design-based estimates are produced for all 50 states and the District of Columbia (DC), as well as 15 Metropolitan Statistical Areas (MSAs). Using public-use microdata, this paper explores the effectiveness of using unit-level model-based estimators that incorporate spatial dependence for the Household Pulse Survey. In particular, we consider Bayesian hierarchical model-based spatial estimates for both a binomial and a multinomial response under informative sampling. Importantly, we demonstrate that these models can be easily estimated using Hamiltonian Monte Carlo through the Stan software package. In doing so, these models can readily be implemented in a production environment. For both the binomial and multinomial responses, an empirical simulation study is conducted, which compares spatial and non-spatial models. Finally, using public-use Household Pulse Survey micro-data, we provide an analysis that compares both design-based and model-based estimators and demonstrates a reduction in standard errors for the model-based approaches.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/jssam/smad020
