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Missing Data Mechanisms and Homogeneity of Means and Variances–Covariances

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Listed:
  • Ke-Hai Yuan

    (Nanjing University of Posts and Telecommunications
    University of Notre Dame)

  • Mortaza Jamshidian

    (California State University, Fullerton)

  • Yutaka Kano

    (Osaka University)

Abstract

Unless data are missing completely at random (MCAR), proper methodology is crucial for the analysis of incomplete data. Consequently, methods for effectively testing the MCAR mechanism become important, and procedures were developed via testing the homogeneity of means and variances–covariances across the observed patterns (e.g., Kim & Bentler in Psychometrika 67:609–624, 2002; Little in J Am Stat Assoc 83:1198–1202, 1988). The current article shows that the population counterparts of the sample means and covariances of a given pattern of the observed data depend on the underlying structure that generates the data, and the normal-distribution-based maximum likelihood estimates for different patterns of the observed sample can converge to the same values even when data are missing at random or missing not at random, although the values may not equal those of the underlying population distribution. The results imply that statistics developed for testing the homogeneity of means and covariances cannot be safely used for testing the MCAR mechanism even when the population distribution is multivariate normal.

Suggested Citation

  • Ke-Hai Yuan & Mortaza Jamshidian & Yutaka Kano, 2018. "Missing Data Mechanisms and Homogeneity of Means and Variances–Covariances," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 425-442, June.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-018-9609-x
    DOI: 10.1007/s11336-018-9609-x
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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. Yuan, Ke-Hai, 2009. "Normal distribution based pseudo ML for missing data: With applications to mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1900-1918, October.
    3. Tang, Man-Lai & Bentler, Peter M., 1998. "Theory and method for constrained estimation in structural equation models with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 27(3), pages 257-270, May.
    4. Jamshidian, Mortaza & Jalal, Siavash & Jansen, Camden, 2014. "MissMech: An R Package for Testing Homoscedasticity, Multivariate Normality, and Missing Completely at Random (MCAR)," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(i06).
    5. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    6. 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.
    7. Annie Qu, 2002. "Testing ignorable missingness in estimating equation approaches for longitudinal data," Biometrika, Biometrika Trust, vol. 89(4), pages 841-850, December.
    8. Ke-Hai Yuan & Wai Chan & Yubin Tian, 2016. "Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 329-351, April.
    9. 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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