Analysis

Description: Survey data typically have missing values due to unit and item nonresponse. Sometimes, survey organizations know the marginal distributions of certain categorical variables in the target population. As shown in previous work, survey organizations can leverage these distributions in multiple imputation for nonignorable unit nonresponse, generating imputations that result in plausible completed-data estimates for the variables with known margins. However, this prior work does not use the design weights for unit nonrespondents. We extend this previous work to utilize the design weights for all sampled units. We illustrate the approach using simulation studies.

Description: Survey data collection often is plagued by unit and item nonresponse. To reduce reliance on strong assumptions about the missingness mechanisms, statisticians can use information about population marginal distributions known, for example, from censuses or administrative databases. One approach that does so is the Missing Data with Auxiliary Margins, or MD-AM, framework, which uses multiple imputation for both unit and item nonresponse so that survey-weighted estimates accord with the known marginal distributions. However, this framework relies on specifying and estimating a joint distribution for the survey data and nonresponse indicators, which can be computationally and practically daunting in data with many variables of mixed types. We propose two adaptations to the MD-AM framework to simplify the imputation task. First, rather than specifying a joint model for unit respondents’ data, we use random hot deck imputation while still leveraging the known marginal distributions. Second, instead of sampling from conditional distributions implied by the joint model for the missing data due to item nonresponse, we apply multiple imputation by chained equations for item nonresponse before imputation for unit nonresponse. Using simulation studies with nonignorable missingness mechanisms, we demonstrate that the proposed approach can provide more accurate point and interval estimates than models that do not leverage the auxiliary information. We illustrate the approach using data on voter turnout from the U.S. Current Population Survey.

Description: When seeking to release public use files for confidential data, statistical agencies can generate fully synthetic data. We propose an approach for making fully synthetic data from surveys collected with complex sampling designs. Our approach adheres to the general strategy proposed by Rubin (1993). Specifically, we generate pseudo-populations by applying the weighted finite population Bayesian bootstrap to account for survey weights, take simple random samples from those pseudo-populations, estimate synthesis models using these simple random samples, and release simulated data drawn from the models as public use files. To facilitate variance estimation, we use the framework of multiple imputation with two data generation strategies. In the first, we generate multiple data sets from each simple random sample. In the second, we generate a single synthetic data set from each simple random sample. We present multiple imputation combining rules for each setting. We illustrate the repeated sampling properties of the combining rules via simulation studies, including comparisons with synthetic data generation based on pseudo-likelihood methods. We apply the proposed methods to a subset of data from the American Community Survey.

Description: We present an approach for imputation of missing items in multivariate categorical data nested within households. The approach relies on a latent class model that (i) allows for household-level and individual-level variables, (ii) ensures that impossible household configurations have zero probability in the model, and (iii) can preserve multivariate distributions both within households and across households. We present a Gibbs sampler for estimating the model and generating imputations. We also describe strategies for improving the computational efficiency of the model estimation. We illustrate the performance of the approach with data that mimic the variables collected in typical population censuses.

Description: We propose an approach for multiple imputation of items missing at random in large-scale surveys with exclusively categorical variables that have structural zeros. Our approach is to use mixtures of multinomial distributions as imputation engines, accounting for structural zeros by conceiving of the observed data as a truncated sample from a hypothetical population without structural zeros. This approach has several appealing features: imputations are generated from coherent, Bayesian joint models that automatically capture complex dependencies and readily scale to large numbers of variables. We outline a Gibbs sampling algorithm for implementing the approach, and we illustrate its potential with a repeated sampling study using public use census microdata from the state of New York, U.S.A.

Description:

To create public use files from large scale surveys, statistical agencies sometimes release random subsamples of the original records. Random subsampling reduces file sizes for secondary data analysts and reduces risks of unintended disclosures of survey participants' confidential information. However, subsampling does not eliminate risks, so that alteration of the data is needed before dissemination. We propose to create disclosure-protected subsamples from large scale surveys based on multiple imputation. The idea is to replace identifying or sensitive values in the original sample with draws from statistical models, and release subsamples of the disclosure-protected data. We present methods for making inferences with the multiple synthetic subsamples.

Description:

The theory of multiple imputation for missing data requires that imputations be made conditional on the sampling design. However, most standard software packages for performing model-based multiple imputation assume simple random samples, leading many practitioners not to account for complex sample design features, such as stratification and clustering, in their imputations. Theory predicts that analyses of such multiply-imputed data sets can yield biased estimates from the design-based perspective. In this article, we illustrate through simulation that (i) the bias can be severe when the design features are related to the survey variables of interest, and (ii) the bias can be reduced by controlling for the design features in the imputation models. The simulations also illustrate that conditioning on irrelevant design features in the imputation models can yield conservative inferences, provided that the models include other relevant predictors. These results suggest a prescription for imputers: the safest course of action is to include design variables in the specification of imputation models. Using real data, we demonstrate a simple approach for incorporating complex design features that can be used with some of the standard software packages for creating multiple imputations.

Description:

Several statistical agencies use, or are considering the use of, multiple imputation to limit the risk of disclosing respondents' identities or sensitive attributes in public use data files. For example, agencies can release partially synthetic datasets, comprising the units originally surveyed with some collected values, such as sensitive values at high risk of disclosure or values of key identifiers, replaced with multiple imputations. This article presents an approach for generating multiply-imputed, partially synthetic datasets that simultaneously handles disclosure limitation and missing data. The basic idea is to fill in the missing data first to generate m completed datasets, then replace sensitive or identifying values in each completed dataset with r imputed values. This article also develops methods for obtaining valid inferences from such multiply-imputed datasets. New rules for combining the multiple point and variance estimates are needed because the double duty of multiple imputation introduces two sources of variability into point estimates, which existing methods for obtaining inferences from multiply-imputed datasets do not measure accurately. A reference t-distribution appropriate for inferences when m and r are moderate is derived using moment matching and Taylor series approximations.

Description:

This paper discusses regression servers, which are data dissemination systems that return some of the output generated by regression analyses in response to user queries. It details work on the special case where the data contain a sensitive variable whose regressions must be protected.

Description:

To avoid disclosures, one approach is to release partially synthetic, public use microdata sets. These comprise the units originally surveyed, but some collected values, for example sensitive values at high risk of disclosure or values of key identifiers, are replaced with multiple imputations. Although partially synthetic approaches are currently used to protect public use data, valid methods of inference have not been developed for them. This article presents such methods. They are based on the concepts of multiple imputation for missing data but use different rules for combining point and variance estimates. The combining rules also differ from those for fully synthetic data sets developed by Raghunathan, Reiter and Rubin (2003). The validity of these new rules is illustrated in simulation studies.

Description: Survey data typically have missing values due to unit and item nonresponse. Sometimes, survey organizations know the marginal distributions of certain categorical variables in the target population. As shown in previous work, survey organizations can leverage these distributions in multiple imputation for nonignorable unit nonresponse, generating imputations that result in plausible completed-data estimates for the variables with known margins. However, this prior work does not use the design weights for unit nonrespondents. We extend this previous work to utilize the design weights for all sampled units. We illustrate the approach using simulation studies.

Description: Survey data collection often is plagued by unit and item nonresponse. To reduce reliance on strong assumptions about the missingness mechanisms, statisticians can use information about population marginal distributions known, for example, from censuses or administrative databases. One approach that does so is the Missing Data with Auxiliary Margins, or MD-AM, framework, which uses multiple imputation for both unit and item nonresponse so that survey-weighted estimates accord with the known marginal distributions. However, this framework relies on specifying and estimating a joint distribution for the survey data and nonresponse indicators, which can be computationally and practically daunting in data with many variables of mixed types. We propose two adaptations to the MD-AM framework to simplify the imputation task. First, rather than specifying a joint model for unit respondents’ data, we use random hot deck imputation while still leveraging the known marginal distributions. Second, instead of sampling from conditional distributions implied by the joint model for the missing data due to item nonresponse, we apply multiple imputation by chained equations for item nonresponse before imputation for unit nonresponse. Using simulation studies with nonignorable missingness mechanisms, we demonstrate that the proposed approach can provide more accurate point and interval estimates than models that do not leverage the auxiliary information. We illustrate the approach using data on voter turnout from the U.S. Current Population Survey.

Description: When seeking to release public use files for confidential data, statistical agencies can generate fully synthetic data. We propose an approach for making fully synthetic data from surveys collected with complex sampling designs. Our approach adheres to the general strategy proposed by Rubin (1993). Specifically, we generate pseudo-populations by applying the weighted finite population Bayesian bootstrap to account for survey weights, take simple random samples from those pseudo-populations, estimate synthesis models using these simple random samples, and release simulated data drawn from the models as public use files. To facilitate variance estimation, we use the framework of multiple imputation with two data generation strategies. In the first, we generate multiple data sets from each simple random sample. In the second, we generate a single synthetic data set from each simple random sample. We present multiple imputation combining rules for each setting. We illustrate the repeated sampling properties of the combining rules via simulation studies, including comparisons with synthetic data generation based on pseudo-likelihood methods. We apply the proposed methods to a subset of data from the American Community Survey.

Description: We present an approach for imputation of missing items in multivariate categorical data nested within households. The approach relies on a latent class model that (i) allows for household-level and individual-level variables, (ii) ensures that impossible household configurations have zero probability in the model, and (iii) can preserve multivariate distributions both within households and across households. We present a Gibbs sampler for estimating the model and generating imputations. We also describe strategies for improving the computational efficiency of the model estimation. We illustrate the performance of the approach with data that mimic the variables collected in typical population censuses.

Description: We propose an approach for multiple imputation of items missing at random in large-scale surveys with exclusively categorical variables that have structural zeros. Our approach is to use mixtures of multinomial distributions as imputation engines, accounting for structural zeros by conceiving of the observed data as a truncated sample from a hypothetical population without structural zeros. This approach has several appealing features: imputations are generated from coherent, Bayesian joint models that automatically capture complex dependencies and readily scale to large numbers of variables. We outline a Gibbs sampling algorithm for implementing the approach, and we illustrate its potential with a repeated sampling study using public use census microdata from the state of New York, U.S.A.

Description:

To create public use files from large scale surveys, statistical agencies sometimes release random subsamples of the original records. Random subsampling reduces file sizes for secondary data analysts and reduces risks of unintended disclosures of survey participants' confidential information. However, subsampling does not eliminate risks, so that alteration of the data is needed before dissemination. We propose to create disclosure-protected subsamples from large scale surveys based on multiple imputation. The idea is to replace identifying or sensitive values in the original sample with draws from statistical models, and release subsamples of the disclosure-protected data. We present methods for making inferences with the multiple synthetic subsamples.

Description:

The theory of multiple imputation for missing data requires that imputations be made conditional on the sampling design. However, most standard software packages for performing model-based multiple imputation assume simple random samples, leading many practitioners not to account for complex sample design features, such as stratification and clustering, in their imputations. Theory predicts that analyses of such multiply-imputed data sets can yield biased estimates from the design-based perspective. In this article, we illustrate through simulation that (i) the bias can be severe when the design features are related to the survey variables of interest, and (ii) the bias can be reduced by controlling for the design features in the imputation models. The simulations also illustrate that conditioning on irrelevant design features in the imputation models can yield conservative inferences, provided that the models include other relevant predictors. These results suggest a prescription for imputers: the safest course of action is to include design variables in the specification of imputation models. Using real data, we demonstrate a simple approach for incorporating complex design features that can be used with some of the standard software packages for creating multiple imputations.

Description:

Several statistical agencies use, or are considering the use of, multiple imputation to limit the risk of disclosing respondents' identities or sensitive attributes in public use data files. For example, agencies can release partially synthetic datasets, comprising the units originally surveyed with some collected values, such as sensitive values at high risk of disclosure or values of key identifiers, replaced with multiple imputations. This article presents an approach for generating multiply-imputed, partially synthetic datasets that simultaneously handles disclosure limitation and missing data. The basic idea is to fill in the missing data first to generate m completed datasets, then replace sensitive or identifying values in each completed dataset with r imputed values. This article also develops methods for obtaining valid inferences from such multiply-imputed datasets. New rules for combining the multiple point and variance estimates are needed because the double duty of multiple imputation introduces two sources of variability into point estimates, which existing methods for obtaining inferences from multiply-imputed datasets do not measure accurately. A reference t-distribution appropriate for inferences when m and r are moderate is derived using moment matching and Taylor series approximations.

Description:

This paper discusses regression servers, which are data dissemination systems that return some of the output generated by regression analyses in response to user queries. It details work on the special case where the data contain a sensitive variable whose regressions must be protected.

Description:

To avoid disclosures, one approach is to release partially synthetic, public use microdata sets. These comprise the units originally surveyed, but some collected values, for example sensitive values at high risk of disclosure or values of key identifiers, are replaced with multiple imputations. Although partially synthetic approaches are currently used to protect public use data, valid methods of inference have not been developed for them. This article presents such methods. They are based on the concepts of multiple imputation for missing data but use different rules for combining point and variance estimates. The combining rules also differ from those for fully synthetic data sets developed by Raghunathan, Reiter and Rubin (2003). The validity of these new rules is illustrated in simulation studies.