Jerome P. Reiter

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.

Many data producers seek to provide users access to confidential data without unduly compromising data subjects' privacy and confidentiality. One general strategy is to require users to do analyses without seeing the confidential data; for example, analysts only get access to synthetic data or query systems that provide disclosure-protected outputs of statistical models. With synthetic data or redacted outputs, the analyst never really knows how much to trust the resulting findings. In particular, if the user did the same analysis on the confidential data, would regression coefficients of interest be statistically significant or not? We present algorithms for assessing this question that satisfy differential privacy. We describe conditions under which the algorithms should give accurate answers about statistical significance. We illustrate the properties of the proposed methods using artificial and genuine data.

We present an approach to inform decisions about nonresponse follow-up sampling. The basic idea is (i) to create completed samples by imputing nonrespondents’ data under various assumptions about the nonresponse mechanisms, (ii) take hypothetical samples of varying sizes from the completed samples, and (iii) compute and compare measures of accuracy and cost for different proposed sample sizes. As part of the methodology, we present a new approach for generating imputations for multivariate continuous data with nonignorable unit nonresponse. We fit mixtures of multivariate normal distributions to the respondents’ data, and adjust the probabilities of the mixture components to generate nonrespondents’ distributions with desired features. We illustrate the approaches using data from the 2007 U.S. Census of Manufactures.

We introduce a nonresponse mechanism for multivariate missing data in which each study variable and its nonresponse indicator are conditionally independent given the remaining variables and their nonresponse indicators. This is a nonignorable missingness mechanism, in that nonresponse for any item can depend on values of other items that are themselves missing. We show that under this itemwise conditionally independent nonresponse assumption, one can define and identify nonparametric saturated classes of joint multivariate models for the study variables and their missingness indicators. We also show how to perform sensitivity analysis with respect to violations of the conditional independence assumptions encoded by this missingness mechanism. We illustrate the proposed modelling approach with data analyses.

Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet Process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. A supplementary material for this article is available online.

We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The model assumes that (i) each group is a member of a group-level latent class, and (ii) each unit is a member of a unit-level latent class nested within its group-level latent class. This structure allows the model to capture dependence among units in the same group. It also facilitates simultaneous modeling of variables at both group and unit levels. We develop a version of the model that assigns zero probability to groups and units with physically impossible combinations of variables. We apply the model to estimate multivariate relationships in a subset of the American Community Survey. Using the estimated model, we generate synthetic household data that could be disseminated as redacted public use files with high analytic validity and low disclosure risks. Supplementary materials for this article are available online.

In some contexts, mixture models can fit certain variables well at the expense of others in ways beyond the analyst's control. For example, when the data include some variables with non-trivial amounts of missing values, the mixture model may fit the marginal distributions of the nearly and fully complete variables at the expense of the variables with high fractions of missing data. Motivated by this setting, we present a mixture model for mixed ordinal and nominal data that splits variables into two groups, focus variables and remainder variables. The model allows the analyst to specify a rich sub-model for the focus variables and a simpler sub-model for remainder variables, yet still capture associations among the variables. Using simulations, we illustrate advantages and limitations of focused clustering compared to mixture models that do not distinguish variables. We apply the model to handle missing values in an analysis of the 2012 American National Election Study, estimating relationships among voting behavior, ideology, and political party affiliation.

We present approaches to generating synthetic microdata for multivariate data that take on non-negative integer values, such as magnitude data in economic surveys. The basic idea is to estimate a mixture of Poisson distributions to describe the multi

Data that include fine geographic information, such as census tract or street block identifiers, can be difficult to release as public use files. Fine geography provides information that ill‐intentioned data users can use to identify individuals. We propose to release data with simulated geographies, so as to enable spatial analyses while reducing disclosure risks. We fit disease mapping models that predict areal‐level counts from attributes in the file and sample new locations based on the estimated models. We illustrate this approach using data on causes of death in North Carolina, including evaluations of the disclosure risks and analytic validity that can result from releasing synthetic geographies. Copyright © 2014 John Wiley & Sons, Ltd.