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Latent variable models with mixed continuous and polytomous data

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  • J.‐Q. Shi
  • S.‐Y. Lee

Abstract

Owing to the nature of the problems and the design of questionnaires, discrete polytomous data are very common in behavioural, medical and social research. Analysing the relationships between the manifest and the latent variables based on mixed polytomous and continuous data has proven to be difficult. A general structural equation model is investigated for these mixed outcomes. Maximum likelihood (ML) estimates of the unknown thresholds and the structural parameters in the covariance structure are obtained. A Monte Carlo–EM algorithm is implemented to produce the ML estimates. It is shown that closed form solutions can be obtained for the M‐step, and estimates of the latent variables are produced as a by‐product of the analysis. The method is illustrated with a real example.

Suggested Citation

  • J.‐Q. Shi & S.‐Y. Lee, 2000. "Latent variable models with mixed continuous and polytomous data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 77-87.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:1:p:77-87
    DOI: 10.1111/1467-9868.00220
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    Cited by:

    1. Sik-Yum Lee & Liang Xu, 2003. "On local influence analysis of full information item factor models," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 339-360, September.
    2. Yang, Qi & He, Haijin & Lu, Bin & Song, Xinyuan, 2022. "Mixture additive hazards cure model with latent variables: Application to corporate default data," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    3. Sik-Yum Lee & Liang Xu, 2003. "Case-Deletion Diagnostics for Factor Analysis Models With Continuous and Ordinal Categorical Data," Sociological Methods & Research, , vol. 31(3), pages 389-419, February.
    4. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R. & Wan, Xiaohai & He, Yulei & Zhang, Kui, 2015. "A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 43-58.
    5. 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.
    6. Lee, Sik-Yum & Song, Xin-Yuan, 2008. "On Bayesian estimation and model comparison of an integrated structural equation model," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4814-4827, June.
    7. Song, Xin-Yuan & Lee, Sik-Yum, 2002. "A Bayesian model selection method with applications," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 539-557, September.
    8. Zhang, Q. & Ip, E.H., 2014. "Variable assessment in latent class models," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 146-156.
    9. An, Xinming & Bentler, Peter M., 2012. "Efficient direct sampling MCEM algorithm for latent variable models with binary responses," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 231-244.
    10. Chunjie Wang & Bo Zhao & Linlin Luo & Xinyuan Song, 2021. "Regression analysis of current status data with latent variables," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 413-436, July.
    11. Celine Marielle Laffont & Marc Vandemeulebroecke & Didier Concordet, 2014. "Multivariate Analysis of Longitudinal Ordinal Data With Mixed Effects Models, With Application to Clinical Outcomes in Osteoarthritis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 955-966, September.
    12. Lee, Sik-Yum & Song, Xin-Yuan, 2003. "Maximum likelihood estimation and model comparison of nonlinear structural equation models with continuous and polytomous variables," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 125-142, October.
    13. Xiang-Nan Feng & Hao-Tian Wu & Xin-Yuan Song, 2017. "Bayesian Adaptive Lasso for Ordinal Regression With Latent Variables," Sociological Methods & Research, , vol. 46(4), pages 926-953, November.
    14. Sik-Yum Lee & Xin-Yuan Song, 2003. "Model comparison of nonlinear structural equation models with fixed covariates," Psychometrika, Springer;The Psychometric Society, vol. 68(1), pages 27-47, March.
    15. Eickhoff, Jens C. & Zhu, Jun & Amemiya, Yasuo, 2004. "On the simulation size and the convergence of the Monte Carlo EM algorithm via likelihood-based distances," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 161-171, April.
    16. Michela Battauz & Ruggero Bellio & Enrico Gori, 2008. "Reducing Measurement Error in Student Achievement Estimation," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 289-302, June.

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