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Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model

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  • Kano, Yutaka
  • Takai, Keiji

Abstract

It is natural to assume that a missing-data mechanism depends on latent variables in the analysis of incomplete data in latent variate modeling because latent variables are error-free and represent key notions investigated by applied researchers. Unfortunately, the missing-data mechanism is then not missing at random (NMAR). In this article, a new estimation method is proposed, which leads to consistent and asymptotically normal estimators for all parameters in a linear latent variate model, where the missing mechanism depends on the latent variables and no concrete functional form for the missing-data mechanism is used in estimation. The method to be proposed is a type of multi-sample analysis with or without mean structures, and hence, it is easy to implement. Complete-case analysis is shown to produce consistent estimators for some important parameters in the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:9:p:1241-1255
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    1. Yiu-Fai Yung & David Thissen & Lori McLeod, 1999. "On the relationship between the higher-order factor model and the hierarchical factor model," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 113-128, June.
    2. William Meredith, 1964. "Notes on factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 177-185, June.
    3. Dantan Etienne & Proust-Lima Cécile & Letenneur Luc & Jacqmin-Gadda Helene, 2008. "Pattern Mixture Models and Latent Class Models for the Analysis of Multivariate Longitudinal Data with Informative Dropouts," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-28, July.
    4. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    5. Ihara, Masamori & Kano, Yutaka, 1995. "Identifiability of full, marginal, and conditional factor analysis models," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 343-350, June.
    6. Bengt Muthén & David Kaplan & Michael Hollis, 1987. "On structural equation modeling with data that are not missing completely at random," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 431-462, September.
    7. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    8. Sik-Yum Lee, 2006. "Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 541-564, September.
    9. A. Mooijaart & P.M. Bentler, 1991. "Robustness of normal theory statistics in structural equation models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(2), pages 159-171, June.
    10. Satorra, Albert, 2002. "Asymptotic Robustness In Multiple Group Linear-Latent Variable Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 297-312, April.
    11. 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.
    12. C. O'Muircheartaigh & I. Moustaki, 1999. "Symmetric pattern models: a latent variable approach to item non‐response in attitude scales," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 177-194.
    13. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    14. Satorra, Albert & Bentler, Peter M., 1990. "Model conditions for asymptotic robustness in the analysis of linear relations," Computational Statistics & Data Analysis, Elsevier, vol. 10(3), pages 235-249, December.
    15. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    16. John Copas & Shinto Eguchi, 2005. "Local model uncertainty and incomplete‐data bias (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 459-513, September.
    17. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    18. Kung‐Yee Liang & Jing Qin, 2000. "Regression analysis under non‐standard situations: a pairwise pseudolikelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 773-786.
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    1. Yuan, Ke-Hai & Savalei, Victoria, 2014. "Consistency, bias and efficiency of the normal-distribution-based MLE: The role of auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 353-370.
    2. 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.

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