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A Bayesian semiparametric dynamic two-level structural equation model for analyzing non-normal longitudinal data

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  • Song, Xin-Yuan
  • Chen, Fei
  • Lu, Zhao-Hua

Abstract

Analyses of non-normal data and longitudinal data to study changes in variables measured repeatedly over time have received considerable attention in social and psychological research. This paper proposes a dynamic two-level nonlinear structural equation model with covariates for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables. To cope with the non-normal continuous data, the corresponding residual errors at both first-level and second-level models are modeled through a Bayesian semiparametric modeling on the basis of a truncated and centered Dirichlet process with stick-breaking priors. The first-level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that vary with time; while the second level is defined for individuals to assess their characteristics that are invariant with time. An algorithm based on the blocked Gibbs sampler is implemented for estimation of parameters. An efficient model comparison statistic, namely the Lν-measure, is also introduced. Results of a simulation study indicate that the performance of the Bayesian semiparametric estimation is satisfactory. The proposed methodologies are applied to a real longitudinal study concerning cocaine use.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:87-108
    DOI: 10.1016/j.jmva.2013.06.001
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    References listed on IDEAS

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    1. Sik-Yum Lee & Ye-Mao Xia, 2006. "Maximum Likelihood Methods in Treating Outliers and Symmetrically Heavy-Tailed Distributions for Nonlinear Structural Equation Models with Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 565-585, September.
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    3. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
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    5. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
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