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Bayesian Approach to Imputing Income Data: Implementation and Evaluation

This study discusses the implementation of Bayesian imputation for income data in EU-SILC dataset, focusing on the variable PY010G. It includes simulations, multiple imputation methods, and evaluation of imputed values compared to initial data. The study also examines the effectiveness of the method and discusses the importance of model selection and handling missing data mechanisms. It highlights the use of SAS software for implementation.

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Bayesian Approach to Imputing Income Data: Implementation and Evaluation

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  1. Implementation of the Bayesian approach to imputation at SORSZvone Klun and Rudi SeljakStatistical Office of the Republic of Slovenia Oslo, September 2012

  2. EU-SILC data • Data on income and living conditions • Data on household members and selected individuals • Among the large number of variables we selected: VARIABLE TO BE IMPUTED • PY010G - Gross annual income • Completely at random deleted about 11% data EXPLANATORY VARIABLES • PE040 - Level of education attained • PL060 - Number of hours usually worked per week • AGE - Age of person

  3. Analysis PY010G • PY010G is very asymmetrical • Analysis according PE040 • Because PE040 is categorical 5 equal models

  4. Further analysis PY010G • For each level of education achieved • Analysis according to AGE and PL060 • For 5th education level

  5. Model for PY010G • Estimations: • Example for: PE040=5, AGE=40, PL060=40 • Graphs of normal distributionwith respect to the data (red) and regression model (green).

  6. Bayes aproach • Equal treatment for • DATA: (PY010G) and • PARAMETERS: • Parameters: • are not fixed values, • have their own probability distribution.

  7. Simulations and Multiple imputation • Simulationsof parameters: • first draw variance: --, • then draw coefficients: • Simulations of missing values (Multiple imputation) • draw missing value: • independently for each missing value(). • 5 imputations almost 98% efficiency (Rubin`s formula for about 11% rate of missing information.)

  8. Imputed values • Example of 5 imputations for: PE040=5, AGE=40, PL060=40

  9. Evaluation • Comparison of the average gross annual income (Initial data: data before deleting.) • Small relative errors • Relatively narrow 95% confidence intervals • Poorer results for model 6, because: • only 58 units • high variance from the linear regression (252862689)

  10. Discussion • Method is effective, • if data are successfully described by the selected model. • Mechanism of missing values is ignorable, if • missing data are MAR and • parameters of model and parameters of mechanism of missing values are divisible (parameters are independent). • Imputed and explanatory variables have to be numerical. • We tested the method progressively by using the SAS programme. • The method is already included in the MCMC procedure in newer version (9.2 and 9.3) of the SAS. Thank you for your attention !

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