Multiple Imputation of Missing or Faulty Values Under Linear Constraints

• Activity Number: 636
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Hang Joon Kim*+ and Jerry Reiter and Quanli Wang and Lawrence Cox and Alan F. Karr
• Companies: Duke University and NISS and Duke University and Duke University and National Institute of Statistical Sciences and National Institute of Statistical Sciences
• Keywords: Edit ; Hit-and-Run ; Mixture ; Nonresponse ; Survey ; Truncation

Abstract

Many statistical agencies collect data that suffer from item nonresponse and erroneous values. Such data also may be required to satisfy a system of linear constraints; some values that do not satisfy the pre-defined constraints are blanked and imputed by statistical agencies. Further, the data may have complex distributional features, including nonlinear relationships and highly non-normal distributions. We present a fully Bayesian, joint model for modeling or imputing data with missing/blanked values under linear constraints that (i) automatically incorporates the constraints in inferences and imputations, and (ii) uses a flexible Dirichlet process mixture of multivariate distributions to reflect complex distributional features. Our basic strategy is to augment the observed data with draws from a hypothetical population in which the constraints are not present, thereby taking advantage of computationally expedient methods for fitting mixture models. Missing/blanked items are sampled from their posterior distribution using the Hit-and-Run sampler, which guarantees that all imputations satisfy the constraints. We illustrate the approach using manufacturing surveys in Colombia.