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A Class of Distribution-Free Models for Longitudinal Mediation Analysis

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  • D. Gunzler
  • W. Tang
  • N. Lu
  • P. Wu
  • X. Tu

Abstract

Mediation analysis constitutes an important part of treatment study to identify the mechanisms by which an intervention achieves its effect. Structural equation model (SEM) is a popular framework for modeling such causal relationship. However, current methods impose various restrictions on the study designs and data distributions, limiting the utility of the information they provide in real study applications. In particular, in longitudinal studies missing data is commonly addressed under the assumption of missing at random (MAR), where current methods are unable to handle such missing data if parametric assumptions are violated. In this paper, we propose a new, robust approach to address the limitations of current SEM within the context of longitudinal mediation analysis by utilizing a class of functional response models (FRM). Being distribution-free, the FRM-based approach does not impose any parametric assumption on data distributions. In addition, by extending the inverse probability weighted (IPW) estimates to the current context, the FRM-based SEM provides valid inference for longitudinal mediation analysis under the two most popular missing data mechanisms; missing completely at random (MCAR) and missing at random (MAR). We illustrate the approach with both real and simulated data. Copyright The Psychometric Society 2014

Suggested Citation

  • D. Gunzler & W. Tang & N. Lu & P. Wu & X. Tu, 2014. "A Class of Distribution-Free Models for Longitudinal Mediation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 543-568, October.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:4:p:543-568
    DOI: 10.1007/s11336-013-9355-z
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    References listed on IDEAS

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    1. Zhiyong Zhang & Lijuan Wang, 2013. "Methods for Mediation Analysis with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 154-184, January.
    2. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    3. Beth Reboussin & Kung-Yee Liang, 1998. "An estimating equations approach for the LISCOMP model," Psychometrika, Springer;The Psychometric Society, vol. 63(2), pages 165-182, June.
    4. Satorra, Albert, 2002. "Asymptotic Robustness In Multiple Group Linear-Latent Variable Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 297-312, April.
    5. Yan Ma & Wan Tang & Qin Yu & X. Tu, 2010. "Modeling Concordance Correlation Coefficient for Longitudinal Study Data," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 99-119, March.
    6. Raymond Hicks & Dustin Tingley, 2011. "Causal mediation analysis," Stata Journal, StataCorp LP, vol. 11(4), pages 605-619, December.
    7. Jeanne Kowalski, 2004. "Nonparametric inference for stochastic linear hypotheses: Application to high-dimensional data," Biometrika, Biometrika Trust, vol. 91(2), pages 393-408, June.
    8. Cora J. M. Maas & Joop J. Hox, 2004. "Robustness issues in multilevel regression analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 127-137, May.
    9. Yan Ma & Wan Tang & Changyong Feng & Xin M. Tu, 2008. "Inference for Kappas for Longitudinal Study Data: Applications to Sexual Health Research," Biometrics, The International Biometric Society, vol. 64(3), pages 781-789, September.
    10. Kowalski J. & Pagano M. & DeGruttola V., 2002. "A Nonparametric Test of Gene Region Heterogeneity Associated With Phenotype," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 398-408, June.
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