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Analysis of multivariate missing data with nonignorable nonresponse

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  • Gong Tang

Abstract

We consider multivariate regression analysis with missing data in the outcome variables, when the nonresponse mechanism depends on the underlying values of the responses and hence is nonignorable. Related problems include response-biased sampling where data are sampled with probability depending only on the univariate response. Our methods do not require specification of the form of the nonresponse mechanism. We show that, under certain regularity conditions, all the regression parameters can be identified from a conditional likelihood based on the complete cases, if the marginal distribution of the covariates is known. If the marginal distribution of the covariates is estimated from the data, then the regression parameters are identified from a pseudolikelihood resulting from substituting the estimated marginal distribution of the covariates in the above conditional likelihood. Simulation studies suggest that the pseudolikelihood method is approximately unbiased. In order to identify the model parameters, usually the dimension of the covariates and observed responses is required to be at least as large as the dimension of the missing responses. The method can also be modified to handle partial information about the missing-data mechanism. We also consider the special case where the missing data have a monotone pattern, where better use of the incomplete information can be made under certain assumptions. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:747-764
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    Citations

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    Cited by:

    1. Laurent Davezies, 2013. "Four Essays in Econometrics," Sciences Po publications info:hdl:2441/6o65lgig8d0, Sciences Po.
    2. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    3. Cui, Xia & Guo, Jianhua & Yang, Guangren, 2017. "On the identifiability and estimation of generalized linear models with parametric nonignorable missing data mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 64-80.
    4. repec:eee:econom:v:202:y:2018:i:2:p:268-285 is not listed on IDEAS
    5. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
    6. Fang, Fang & Shao, Jun, 2016. "Iterated imputation estimation for generalized linear models with missing response and covariate values," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 111-123.
    7. Li-Chun Zhang & Ib Thomsen & Øyvin Kleven, 2013. "On the Use of Auxiliary and Paradata for Dealing With Non-sampling Errors in Household Surveys," International Statistical Review, International Statistical Institute, vol. 81(2), pages 270-288, August.
    8. Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    9. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2017. "Nonparametric Estimation in Case of Endogenous Selection," Rationality and Competition Discussion Paper Series 58, CRC TRR 190 Rationality and Competition.
    10. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    11. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
    12. repec:spo:wpecon:info:hdl:2441/6o65lgig8d0qcro9p14826c84 is not listed on IDEAS
    13. Laurent Davezies & Xavier d'Haultfoeuille, 2013. "Endogenous Attrition in Panels," Working Papers 2013-17, Center for Research in Economics and Statistics.
    14. 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.
    15. Chen, Qingxia & Ibrahim, Joseph G. & Chen, Ming-Hui & Senchaudhuri, Pralay, 2008. "Theory and inference for regression models with missing responses and covariates," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1302-1331, July.
    16. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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