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Multiple imputation of ordinal missing not at random data

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  • Angelina Hammon

    (German Institute for Economic Research (DIW Berlin)
    University of Bamberg)

Abstract

We introduce a selection model-based imputation approach to be used within the Fully Conditional Specification (FCS) framework for the Multiple Imputation (MI) of incomplete ordinal variables that are supposed to be Missing Not at Random (MNAR). Thereby, we generalise previous work on this topic which involved binary single-level and multilevel data to ordinal variables. We apply an ordered probit model with sample selection as base of our imputation algorithm. The applied model involves two equations that are modelled jointly where the first one describes the missing-data mechanism and the second one specifies the variable to be imputed. In addition, we develop a version for hierarchical data by incorporating random intercept terms in both equations. To fit this multilevel imputation model we use quadrature techniques. Two simulation studies validate the overall good performance of our single-level and multilevel imputation methods. In addition, we show its applicability to empirical data by applying it to a common research topic in educational science using data of the National Educational Panel Study (NEPS) and conducting a short sensitivity analysis. Our approach is designed to be used within the R software package mice which makes it easy to access and apply.

Suggested Citation

  • Angelina Hammon, 2023. "Multiple imputation of ordinal missing not at random data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(4), pages 671-692, December.
    • Handle: RePEc:spr:alstar:v:107:y:2023:i:4:d:10.1007_s10182-022-00461-9
    DOI: 10.1007/s10182-022-00461-9
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    References listed on IDEAS

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    1. Jian Zhu & Trivellore E. Raghunathan, 2015. "Convergence Properties of a Sequential Regression Multiple Imputation Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1112-1124, September.
    2. Hammon, Angelina & Zinn, Sabine, 2020. "Multiple imputation of binary multilevel missing not at random data," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 69(3), pages 547-564.
    3. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
    4. Angelina Hammon & Sabine Zinn, 2020. "Multiple imputation of binary multilevel missing not at random data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 547-564, June.
    5. Ulrich Rendtel, 1992. "On the Choice of a Selection-Model When Estimating Regressionmodels with Selectivity," Discussion Papers of DIW Berlin 53, DIW Berlin, German Institute for Economic Research.
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    Cited by:

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