Search for: All records

Abstract The Household Pulse Survey (HPS), released by the US Census Bureau at the start of the coronavirus pandemic, gathers timely information about the societal and economic impacts of coronavirus. The first phase of the survey was launched in April 2020 and ran for 12 weeks. To track the immediate impact of the pandemic, individual respondents during this phase were re-sampled for up to three consecutive weeks. Motivated by expected job loss during the pandemic, using public-use microdata, this work proposes unit-level, model-based estimators that incorporate longitudinal dependence at both the response and domain level. In particular, using a pseudo-likelihood, we consider a Bayesian hierarchical unit-level, model-based approach for both Gaussian and binary response data under informative sampling. To facilitate construction of these model-based estimates, we develop an efficient Gibbs sampler. An empirical simulation study is conducted to compare the proposed approach to models that do not account for unit-level longitudinal correlation. Finally, using public-use HPS micro-data, we provide an analysis of ‘expected job loss’ that compares both design- and model-based estimators and demonstrates superior performance for the proposed model-based approaches. 

Small area estimation models are critical for dissemination and understanding of important population characteristics within sub-domains that often have limited sample size. The classic Fay-Herriot model is perhaps the most widely used approach to generate such estimates. However, a limiting assumption of this approach is that the latent true population quantity has a linear relationship with the given covariates. Through the use of random weight neural networks, we develop a Bayesian hierarchical extension of this framework that allows for estimation of nonlinear relationships between the true population quantity and the covariates. We illustrate our approach through an empirical simulation study as well as an analysis of median household income for census tracts in the state of California. 

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. 

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. 

Abstract The topic of neural networks has seen a surge of interest in recent years. However, one of the main challenges with these approaches is quantification of uncertainty. The use of random weight models offer a potential solution. In addition to uncertainty quantification, these models are extremely computationally efficient as they do not require optimisation through stochastic gradient descent. We show how this approach can be used to account for informative sampling of survey data through the use of a pseudo-likelihood. We illustrate the effectiveness of this methodology through simulation and data application involving American National Election Studies data. 

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. 

Abstract Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in multivariate settings. In addition, we make use of a variety of Bayesian modeling techniques to ensure that the model is fit in a computationally efficient manner. We illustrate the value of our approach through two simulation studies as well as an example of mortality estimation using NHANES data.