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Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence

Publication ,  Journal Article
Murray, JS; Reiter, JP
Published in: Journal of the American Statistical Association
October 1, 2016

We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures of multinomial distributions for categorical variables with Dirichlet process mixtures of multivariate normal distributions for continuous variables. We incorporate dependence between the continuous and categorical variables by (1) modeling the means of the normal distributions as component-specific functions of the categorical variables and (2) forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model. This structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst. We apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the Survey of Income and Program Participation (SIPP). The goal is to compare estimates from a field test with the new design to estimates from selected individuals from a panel collected under the old design. We show that accounting for the missing data changes some conclusions about the comparability of the distributions in the two datasets. We also perform an extensive repeated sampling simulation using similar data from complete cases in an existing SIPP panel, comparing our proposed model to a default application of multiple imputation by chained equations. Imputations based on the proposed model tend to have better repeated sampling properties than the default application of chained equations in this realistic setting. Supplementary materials for this article are available online.

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Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 1, 2016

Volume

111

Issue

516

Start / End Page

1466 / 1479

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

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Murray, J. S., & Reiter, J. P. (2016). Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence. Journal of the American Statistical Association, 111(516), 1466–1479. https://doi.org/10.1080/01621459.2016.1174132
Murray, J. S., and J. P. Reiter. “Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence.” Journal of the American Statistical Association 111, no. 516 (October 1, 2016): 1466–79. https://doi.org/10.1080/01621459.2016.1174132.
Murray JS, Reiter JP. Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence. Journal of the American Statistical Association. 2016 Oct 1;111(516):1466–79.
Murray, J. S., and J. P. Reiter. “Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence.” Journal of the American Statistical Association, vol. 111, no. 516, Oct. 2016, pp. 1466–79. Scopus, doi:10.1080/01621459.2016.1174132.
Murray JS, Reiter JP. Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence. Journal of the American Statistical Association. 2016 Oct 1;111(516):1466–1479.

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

October 1, 2016

Volume

111

Issue

516

Start / End Page

1466 / 1479

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics