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Missing Data Imputation Using the Multivariate t Distribution

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  • Liu, C.

Abstract

When a rectangular multivariate data set contains missing values, missing data imputation using the multivariate t distribution appears potentially useful, especially for robust inferences. An efficient technique, called the monotone data augmentation algorithm, for implementing missing data imputation using the multivariate t distribution with known and unknown weights, with monotone and nonmonotone missing data, and with known and unknown degrees of freedom is presented. Two numerical examples are included to illustrate the methodology, to compare results obtained using the multivariate t distribution with results obtained using the normal distribution, and to compare the rate of convergence of the monotone data augmentation algorithm with the rate of convergence of the (rectangular) data augmentation algorithm.

Suggested Citation

  • Liu, C., 1995. "Missing Data Imputation Using the Multivariate t Distribution," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 139-158, April.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:139-158
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    Cited by:

    1. Margarita Marín & Edilberto Cepeda-Cuervo, 2022. "A Bayesian Regression Model for the Non-standardized t Distribution with Location, Scale and Degrees of Freedom Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 809-830, November.
    2. Tang, Yongqiang, 2015. "An efficient monotone data augmentation algorithm for Bayesian analysis of incomplete longitudinal data," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 146-152.
    3. Fernández, C. & Steel, M.F.J., 1997. "Multivariate Student -t Regression Models : Pitfalls and Inference," Discussion Paper 1997-08, Tilburg University, Center for Economic Research.
    4. Jie Jiang & Xinsheng Liu & Keming Yu, 2013. "Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution," Computational Statistics, Springer, vol. 28(4), pages 1485-1500, August.
    5. M.J. Daniels & C. Wang & B.H. Marcus, 2014. "Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates," Biometrics, The International Biometric Society, vol. 70(1), pages 62-72, March.
    6. Margaret Y Hwang & David Weil, 1997. "The Diffusion of Modern Manufacturing Practices: Evidence from Retail-Apparel Sectors," Working Papers 97-11, Center for Economic Studies, U.S. Census Bureau.
    7. Atkinson, A. C. & Cheng, Tsung-Chi, 2000. "On robust linear regression with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 33(4), pages 361-380, June.
    8. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    9. Sik-Yum Lee & Ye-Mao Xia, 2008. "A Robust Bayesian Approach for Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 343-364, September.

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