Hierarchical Bayesian Nonresponse Models for Binary Data From Small Areas With Uncertainty About Ignorability

In small area estimation, it is a standard practice to assume that the area effects are exchangeable. This is obtained by assuming that the area effects have a common parametric distribution, and a Bayesian approach is attractive. The Dirichlet process prior (DPP) has been used to provide a nonparametric version of this approach. The DPP is useful because it makes the procedure more robust, and the Bayesian approach helps to reduce the effect of nonidentifiability prominent in nonignorable nonresponse models. Using the DPP, we develop a Bayesian methodology for the analysis of nonignorable nonresponse binary data from many small areas, and for each area, we estimate the proportion of individuals with a particular characteristic. Our DPP model is centered on a baseline model, a standard parametric model. We use Markov chain Monte Carlo methods to fit the DPP model and the baseline model, and our methodology is illustrated using data on victimization in ten domains from the National Crime Survey. Our comparisons show that it may be preferable to use the nonparametric DPP model over the parametric baseline model for the analysis of these data.

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“…We note that this information was not incorporated into the models of Stasny (1991) and Nandram and Choi (2002a).…”

Section: National Crime Surveymentioning

confidence: 95%

Nonparametric Bayesian analysis of a proportion for a small area under nonignorable nonresponse

Nandram

Choi

2004

Journal of Nonparametric Statistics

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“…Posterior formulas are shown for both an ignorable and nonignorable model. Nandrum and Choi (2002) follow up this article by taking a full Bayesian approach. Again, both the ignorable and nonignorable models are examined.…”

Section: Modelmentioning

confidence: 99%

“…This is followed up in Nandrum and Choi (2002), who use a fully Bayesian approach. The work presented in these articles does not, however, take into account potential spatial relationships among domains.…”

Section: Introductionmentioning

confidence: 99%

“…Lesser and Kalsbeek (1999) discuss nonresponse adjustment techniques for three environmental surveys. Bayesian nonresponse approaches have been examined in Kaufman and King (1973), Basu and de B. Pereira (1982), Stasny (1991), Nandrum and Choi (2002), and Qin et al (2002). Gunel (1984) also approached how to select a sample size among the nonrespondents.…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Bayesian Modeling in Dichotomous Processes in the Presence of Nonresponse

Oleson

He²

2004

Biometrics

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Sampling units that do not answer a survey may dramatically affect the estimation results of interest. The response may even be conditional on the outcome of interest in the survey. If estimates are found using only those who responded, the estimate may be biased, known as nonresponse bias. We are interested in finding estimates of success rates from a survey. We begin by looking at two current Bayesian approaches to treating nonresponse in a hierarchical model. However, these approaches do not consider possible spatial correlations between domains for either success rate or response rate. We build a Bayesian hierarchical spatial model to explicitly estimate the success rate, response rate given success, and response rate given failure. The success rates in the domains of the survey are allowed to be spatially correlated. We also allow spatial dependence between domains in both response rate given success and response rate given failure. Spatial dependence is induced by a common latent spatial structure between the two conditional response rates. We use the 1998 Missouri Turkey Hunting Survey to illustrate this methodology. We find significant spatial correlation in the success rates and incorporating nonrespondents has an impact on the success rate estimates.

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“…Nandram and Choi (2002) used an expansion model to study nonignorable nonresponse binary data and Nandram and Katzoff (2012) used a similar model for polychotomous data.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Small Area Models for Three-way Contingency Tables with Nonignorability

Kim¹,

Woo²,

Nandram³

2018

STAT SINICA

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We show how to use Bayesian uncertainty analysis to study several three-way contingency tables, each obtained from a single area, when one, two or three categories are missing. This is an extension of Nandram and Woo (2015) to cover small areas. One approach to analyze these data is to construct several tables (one complete and the others incomplete) with each table corresponding to one or more missing categories. When tables are incomplete and nonignorable nonresponse models are used, there are nonidentifiable parameters. To deal with these parameters, we describe five hierarchical Bayesian models, which are an ignorable nonresponse model and four nonignorable nonresponse models. Rather than performing a sensitivity analysis, we perform the Bayesian uncertainty analysis by placing priors on the nonidentifiable parameters. This is done to reduce the effects of the nonidentifiable parameters that is accomplished by projecting the parameters to a lower dimensional space and allowing the reduced set of parameters to share a common distribution. Also, this procedure allows a "borrowing of strength" from larger areas to improve estimation in smaller areas. We use the griddy Gibbs sampler to fit our models and we use goodness-of-fit procedures to assess model fit. We use an illustrative example and a simulation study to compare our models when inference is made about finite population proportions of the cells of the three-way tables.

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Hierarchical Bayesian Nonresponse Models for Binary Data From Small Areas With Uncertainty About Ignorability

Cited by 34 publications

References 30 publications

Nonparametric Bayesian analysis of a proportion for a small area under nonignorable nonresponse

Nonparametric Bayesian analysis of a proportion for a small area under nonignorable nonresponse

Hierarchical Bayesian Modeling in Dichotomous Processes in the Presence of Nonresponse

Bayesian Small Area Models for Three-way Contingency Tables with Nonignorability

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