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Diagnostic Test for Realized Missingness in Mixed-type Data

Author

Listed:
  • Ruizhe Chen

    (Johns Hopkins University)

  • Yu-Che Chung

    (Takeda Pharmaceuticals)

  • Sanjib Basu

    (University of Illinois Chicago)

  • Qian Shi

    (Mayo Clinic)

Abstract

A frequent concern in analyzing incomplete multivariate measurements in mixed categorical and quantitative scales is whether missing completely at random (MCAR) is an appropriate model. Realized MCAR refers to constancy of conditional probability at realized missing data patterns and differs from always MCAR. We develop a scalable approach for diagnostics of realized MCAR in mixed-type data for which existing methods are lacking. We interestingly establish that the null framework may hold under the broader condition of observed at random (OAR) under component independence and the method cannot detect departure in the direction of OAR under independence but may do so under dependence. We demonstrate that the proposed method is easy to implement and scalable. In the special case of non-mixed type data, we face computational difficulties with existing methods whereas the proposed approach performs superiorly. The proposed approach is applied to analyze incomplete mixed-type data from the ARCAD metastatic colorectal cancer database.

Suggested Citation

  • Ruizhe Chen & Yu-Che Chung & Sanjib Basu & Qian Shi, 2024. "Diagnostic Test for Realized Missingness in Mixed-type Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 109-138, May.
    • Handle: RePEc:spr:sankhb:v:86:y:2024:i:1:d:10.1007_s13571-023-00317-5
    DOI: 10.1007/s13571-023-00317-5
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    References listed on IDEAS

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    1. Mortaza Jamshidian & Siavash Jalal, 2010. "Tests of Homoscedasticity, Normality, and Missing Completely at Random for Incomplete Multivariate Data," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 649-674, December.
    2. Fabrizia Mealli & Donald B. Rubin, 2015. "Clarifying missing at random and related definitions, and implications when coupled with exchangeability," Biometrika, Biometrika Trust, vol. 102(4), pages 995-1000.
    3. Jun Li & Yao Yu, 2015. "A Nonparametric Test of Missing Completely at Random for Incomplete Multivariate Data," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 707-726, September.
    4. Iavor I Bojinov & Natesh S Pillai & Donald B Rubin, 2020. "Diagnosing missing always at random in multivariate data," Biometrika, Biometrika Trust, vol. 107(1), pages 246-253.
    5. Kevin Kim & Peter Bentler, 2002. "Tests of homogeneity of means and covariance matrices for multivariate incomplete data," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 609-623, December.
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