IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i9p2031-2043.html
   My bibliography  Save this article

Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models

Author

Listed:
  • Tang, Nian-Sheng
  • Chen, Xing
  • Fu, Ying-Zi

Abstract

Non-linear structural equation models are widely used to analyze the relationships among outcomes and latent variables in modern educational, medical, social and psychological studies. However, the existing theories and methods for analyzing non-linear structural equation models focus on the assumptions of outcomes from an exponential family, and hence can't be used to analyze non-exponential family outcomes. In this paper, a Bayesian method is developed to analyze non-linear structural equation models in which the manifest variables are from a reproductive dispersion model (RDM) and/or may be missing with non-ignorable missingness mechanism. The non-ignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is used to obtain the joint Bayesian estimates of structural parameters, latent variables and parameters in the logistic regression model, and a procedure calculating the Bayes factor for model comparison is given via path sampling. A goodness-of-fit statistic is proposed to assess the plausibility of the posited model. A simulation study and a real example are presented to illustrate the newly developed Bayesian methodologies.

Suggested Citation

  • Tang, Nian-Sheng & Chen, Xing & Fu, Ying-Zi, 2009. "Bayesian analysis of non-linear structural equation models with non-ignorable missing outcomes from reproductive dispersion models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2031-2043, October.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:2031-2043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00095-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Tang, Nian-Sheng & Wei, Bo-Cheng & Wang, Xue-Ren, 2000. "Influence diagnostics in nonlinear reproductive dispersion models," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 59-68, January.
    3. Sik-Yum Lee & Xin-Yuan Song, 2003. "Maximum Likelihood Estimation and Model Comparison for Mixtures of Structural Equation Models with Ignorable Missing Data," Journal of Classification, Springer;The Classification Society, vol. 20(2), pages 221-255, September.
    4. Sik-Yum Lee & Hong-Tu Zhu, 2002. "Maximum likelihood estimation of nonlinear structural equation models," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 189-210, June.
    5. Peter Xue-Kun Song & Ming Tan, 2000. "Marginal Models for Longitudinal Continuous Proportional Data," Biometrics, The International Biometric Society, vol. 56(2), pages 496-502, June.
    6. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Le–Le Zou, 2012. "The impacting factors of vulnerability to natural hazards in China: an analysis based on structural equation model," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 62(1), pages 57-70, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Xue-Dong & Tang, Nian-Sheng, 2010. "Bayesian analysis of semiparametric reproductive dispersion mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2145-2158, September.
    2. Sik-Yum Lee & Xin-Yuan Song, 2007. "A Unified Maximum Likelihood Approach for Analyzing Structural Equation Models With Missing Nonstandard Data," Sociological Methods & Research, , vol. 35(3), pages 352-381, February.
    3. Fu, Ying-Zi & Tang, Nian-Sheng & Chen, Xing, 2009. "Local influence analysis of nonlinear structural equation models with nonignorable missing outcomes from reproductive dispersion models," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3671-3684, August.
    4. England, Peter, 2002. "Addendum to "Analytic and bootstrap estimates of prediction errors in claims reserving"," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 461-466, December.
    5. Ruixin Guo & Hongtu Zhu & Sy-Miin Chow & Joseph G. Ibrahim, 2012. "Bayesian Lasso for Semiparametric Structural Equation Models," Biometrics, The International Biometric Society, vol. 68(2), pages 567-577, June.
    6. Nathaniel Tomasetti & Catherine Forbes & Anastasios Panagiotelis, 2019. "Updating Variational Bayes: Fast Sequential Posterior Inference," Monash Econometrics and Business Statistics Working Papers 13/19, Monash University, Department of Econometrics and Business Statistics.
    7. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, September.
    8. Song, Xin-Yuan & Chen, Fei & Lu, Zhao-Hua, 2013. "A Bayesian semiparametric dynamic two-level structural equation model for analyzing non-normal longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 87-108.
    9. Tang, Niansheng & Wang, Wenjun, 2019. "Robust estimation of generalized estimating equations with finite mixture correlation matrices and missing covariates at random for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 640-655.
    10. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "Determinants of bid and ask quotes and implications for the cost of trading," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 656-678, September.
    11. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    12. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    13. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    14. Sabiwalsky, Ralf, 2008. "Nonlinear modeling of target leverage with latent determinant variables: New evidence on the trade-off theory," SFB 649 Discussion Papers 2008-062, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Li, Kan & Luo, Sheng, 2019. "Bayesian functional joint models for multivariate longitudinal and time-to-event data," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 14-29.
    16. Ahmed Mustafa & Xiao Wei Zhang & Daniel G Aliaga & Martin Bruwier & Gen Nishida & Benjamin Dewals & Sébastian Erpicum & Pierre Archambeau & Michel Pirotton & Jacques Teller, 2020. "Procedural generation of flood-sensitive urban layouts," Environment and Planning B, , vol. 47(5), pages 889-911, June.
    17. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    18. Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    19. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    20. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:2031-2043. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.