Browsing by Subject "Latent"

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Open Access
An Empirical Comparison of Multiple Imputation Methods for Categorical Data
(The American Statistician, 2017-04-03) Akande, O; Li, F; Reiter, J
© 2017 American Statistical Association. 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. Supplementary material for this article is available online.
Open Access
Dirichlet Process Mixture Models for Nested Categorical Data
(2015) Hu, Jingchen
This thesis develops Bayesian latent class models for nested categorical data, e.g., people nested in households. The applications focus on generating synthetic microdata for public release and imputing missing data for household surveys, such as the 2010 U.S. Decennial Census.
The first contribution is methods for evaluating disclosure risks in fully synthetic categorical data. I quantify disclosure risks by computing Bayesian posterior probabilities that intruders can learn confidential values given the released data and assumptions about their prior knowledge. I demonstrate the methodology on a subset of data from the American Community Survey (ACS). The methods can be adapted to synthesizers for nested data, as demonstrated in later chapters of the thesis.
The second contribution is a novel two-level latent class model for nested categorical data. Here, I assume that all configurations of groups and units are theoretically possible. I use a nested Dirichlet Process prior distribution for the class membership probabilities. The nested structure facilitates simultaneous modeling of variables at both group and unit levels. I illustrate the modeling by generating synthetic data and imputing missing data for a subset of data from the 2012 ACS household data. I show that the model can capture within group relationships more effectively than standard one-level latent class models.
The third contribution is a version of the nested latent class model adapted for theoretically impossible combinations, e.g. a household with two household heads or a child older than her biological father. This version assigns zero probability to those impossible groups and units. I present a proof that the Markov Chain Monte Carlo (MCMC) sampling strategy estimates the desired target distribution. I illustrate this model by generating synthetic data and imputing missing data for a subset of data from the 2011 ACS household data. The results indicate that this version can estimate the joint distribution more effectively than the previous version.
Open Access
Simultaneous Edit and Imputation for Household Data with Structural Zeros
(Journal of Survey Statistics and Methodology) Akande, Olanrewaju; Barrientos, Andres; Reiter, Jerome
Multivariate categorical data nested within households often include reported values that fail edit constraints---for example, a participating household reports a child's age as older than his biological parent's age---as well as missing values. Generally, agencies prefer datasets to be free from erroneous or missing values before analyzing them or disseminating them to secondary data users. We present a model-based engine for editing and imputation of household data based on a Bayesian hierarchical model that includes (i) a nested data Dirichlet process mixture of products of multinomial distributions as the model for the true latent values of the data, truncated to allow only households that satisfy all edit constraints, (ii) a model for the location of errors, and (iii) a reporting model for the observed responses in error. The approach propagates uncertainty due to unknown locations of errors and missing values, generates plausible datasets that satisfy all edit constraints, and can preserve multivariate relationships within and across individuals in the same household. We illustrate the approach using data from the 2012 American Community Survey.