Using the conditional grade-of-membership model to assess judgment accuracy

Cooil, Bruce; Varki, Sajeev

doi:10.1007/bf02294737

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…GoM models belong to the general class of mixed membership models (Erosheva, 2002; Erosheva et al, 2004), in which individuals are allowed membership in more than one class simultaneously. Models from this family have been proposed for a wide range of applications, including the study of disability among elders (Manton et al, 1994; Erosheva et al, 2007), network analysis (Airoldi et al, 2008), electoral preferences analysis (Gormley, 2006; Gormley and Murphy, 2008), estimation of judgment accuracy (Cooil and Varki, 2003), estimation of population sizes (Manrique-Vallier and Fienberg, 2008), genetic composition analysis (Pritchard et al, 2000) and text classification (Erosheva et al, 2004; Blei et al, 2003; Blei and Lafferty, 2007). Like other latent structure models, mixed membership models offer an approach to the analysis of large, sparse contingency tables with complex interactions.…”

Section: Grade Of Membership Modelsmentioning

confidence: 99%

Estimating Identification Disclosure Risk Using Mixed Membership Models

Manrique-Vallier

Reiter

2012

Journal of the American Statistical Association

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Statistical agencies and other organizations that disseminate data are obligated to protect data subjects’ confidentiality. For example, ill-intentioned individuals might link data subjects to records in other databases by matching on common characteristics (keys). Successful links are particularly problematic for data subjects with combinations of keys that are unique in the population. Hence, as part of their assessments of disclosure risks, many data stewards estimate the probabilities that sample uniques on sets of discrete keys are also population uniques on those keys. This is typically done using log-linear modeling on the keys. However, log-linear models can yield biased estimates of cell probabilities for sparse contingency tables with many zero counts, which often occurs in databases with many keys. This bias can result in unreliable estimates of probabilities of uniqueness and, hence, misrepresentations of disclosure risks. We propose an alternative to log-linear models for datasets with sparse keys based on a Bayesian version of grade of membership (GoM) models. We present a Bayesian GoM model for multinomial variables and offer an MCMC algorithm for fitting the model. We evaluate the approach by treating data from a recent US Census Bureau public use microdata sample as a population, taking simple random samples from that population, and benchmarking estimated probabilities of uniqueness against population values. Compared to log-linear models, GoM models provide more accurate estimates of the total number of uniques in the samples. Additionally, they offer record-level predictions of uniqueness that dominate those based on log-linear models.

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