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• 1. Bayesian predictive inference of small area proportions under selection bias

  Articles and reports: 12-001-X202100100001

  Description:

  In a previous paper, we developed a model to make inference about small area proportions under selection bias in which the binary responses and the selection probabilities are correlated. This is the homogeneous nonignorable selection model; nonignorable selection means that the selection probabilities and the binary responses are correlated. The homogeneous nonignorable selection model was shown to perform better than a baseline ignorable selection model. However, one limitation of the homogeneous nonignorable selection model is that the distributions of the selection probabilities are assumed to be identical across areas. Therefore, we introduce a more general model, the heterogeneous nonignorable selection model, in which the selection probabilities are not identically distributed over areas. We used Markov chain Monte Carlo methods to fit the three models. We illustrate our methodology and compare our models using an example on severe activity limitation of the U.S. National Health Interview Survey. We also perform a simulation study to demonstrate that our heterogeneous nonignorable selection model is needed when there is moderate to strong selection bias.

  Release date: 2021-06-24

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• 2. Bayesian predictive inference of a proportion under a two-fold small area model with heterogeneous correlations Archived

  Articles and reports: 12-001-X201700114822

  Description:

  We use a Bayesian method to infer about a finite population proportion when binary data are collected using a two-fold sample design from small areas. The two-fold sample design has a two-stage cluster sample design within each area. A former hierarchical Bayesian model assumes that for each area the first stage binary responses are independent Bernoulli distributions, and the probabilities have beta distributions which are parameterized by a mean and a correlation coefficient. The means vary with areas but the correlation is the same over areas. However, to gain some flexibility we have now extended this model to accommodate different correlations. The means and the correlations have independent beta distributions. We call the former model a homogeneous model and the new model a heterogeneous model. All hyperparameters have proper noninformative priors. An additional complexity is that some of the parameters are weakly identified making it difficult to use a standard Gibbs sampler for computation. So we have used unimodal constraints for the beta prior distributions and a blocked Gibbs sampler to perform the computation. We have compared the heterogeneous and homogeneous models using an illustrative example and simulation study. As expected, the two-fold model with heterogeneous correlations is preferred.

  Release date: 2017-06-22

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• 3. Hierarchical and empirical Bayes small domain estimation of the proportion of persons without health insurance for minority subpopulations Archived

  Articles and reports: 12-001-X200900110884

  Description:

  The paper considers small domain estimation of the proportion of persons without health insurance for different minority groups. The small domains are cross-classified by age, sex and other demographic characteristics. Both hierarchical and empirical Bayes estimation methods are used. Also, second order accurate approximations of the mean squared errors of the empirical Bayes estimators and bias-corrected estimators of these mean squared errors are provided. The general methodology is illustrated with estimates of the proportion of uninsured persons for several cross-sections of the Asian subpopulation.

  Release date: 2009-06-22

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Articles and reports (3) ((3 results))

• 1. Bayesian predictive inference of small area proportions under selection bias

  Articles and reports: 12-001-X202100100001

  Description:

  In a previous paper, we developed a model to make inference about small area proportions under selection bias in which the binary responses and the selection probabilities are correlated. This is the homogeneous nonignorable selection model; nonignorable selection means that the selection probabilities and the binary responses are correlated. The homogeneous nonignorable selection model was shown to perform better than a baseline ignorable selection model. However, one limitation of the homogeneous nonignorable selection model is that the distributions of the selection probabilities are assumed to be identical across areas. Therefore, we introduce a more general model, the heterogeneous nonignorable selection model, in which the selection probabilities are not identically distributed over areas. We used Markov chain Monte Carlo methods to fit the three models. We illustrate our methodology and compare our models using an example on severe activity limitation of the U.S. National Health Interview Survey. We also perform a simulation study to demonstrate that our heterogeneous nonignorable selection model is needed when there is moderate to strong selection bias.

  Release date: 2021-06-24

  ---

• 2. Bayesian predictive inference of a proportion under a two-fold small area model with heterogeneous correlations Archived

  Articles and reports: 12-001-X201700114822

  Description:

  We use a Bayesian method to infer about a finite population proportion when binary data are collected using a two-fold sample design from small areas. The two-fold sample design has a two-stage cluster sample design within each area. A former hierarchical Bayesian model assumes that for each area the first stage binary responses are independent Bernoulli distributions, and the probabilities have beta distributions which are parameterized by a mean and a correlation coefficient. The means vary with areas but the correlation is the same over areas. However, to gain some flexibility we have now extended this model to accommodate different correlations. The means and the correlations have independent beta distributions. We call the former model a homogeneous model and the new model a heterogeneous model. All hyperparameters have proper noninformative priors. An additional complexity is that some of the parameters are weakly identified making it difficult to use a standard Gibbs sampler for computation. So we have used unimodal constraints for the beta prior distributions and a blocked Gibbs sampler to perform the computation. We have compared the heterogeneous and homogeneous models using an illustrative example and simulation study. As expected, the two-fold model with heterogeneous correlations is preferred.

  Release date: 2017-06-22

  ---

• 3. Hierarchical and empirical Bayes small domain estimation of the proportion of persons without health insurance for minority subpopulations Archived

  Articles and reports: 12-001-X200900110884

  Description:

  The paper considers small domain estimation of the proportion of persons without health insurance for different minority groups. The small domains are cross-classified by age, sex and other demographic characteristics. Both hierarchical and empirical Bayes estimation methods are used. Also, second order accurate approximations of the mean squared errors of the empirical Bayes estimators and bias-corrected estimators of these mean squared errors are provided. The general methodology is illustrated with estimates of the proportion of uninsured persons for several cross-sections of the Asian subpopulation.

  Release date: 2009-06-22

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