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Author: Song, Xinyuan
Resulting in 2 citations.
1. Liu, Hefei
Song, Xinyuan
Bayesian Analysis of Hidden Markov Structural Equation Models with an Unknown Number of Hidden States
Econometrics and Statistics published online (21 May 2020): DOI: 10.1016/j.ecosta.2020.03.003.
Also: https://www.sciencedirect.com/science/article/pii/S2452306220300356
Cohort(s): Children of the NLSY79, NLSY79
Publisher: Elsevier
Keyword(s): Bayesian; Behavior Problems Index (BPI); Modeling, Structural Equation; Parent-Child Relationship/Closeness; Parenting Skills/Styles; Peabody Individual Achievement Test (PIAT- Math); Peabody Individual Achievement Test (PIAT- Reading)

Hidden Markov models (HMMs) are widely used to analyze heterogeneous longitudinal data owing to their capability to model dynamic heterogeneity. Early advancements in HMMs have mainly assumed that the number of hidden states is fixed and predetermined based on the knowledge of the subjects or a certain criterion. However, as a limitation, this approach determines the number of hidden states on a pairwise basis, which becomes increasingly tedious when the state space is enlarged. Moreover, criterion-based statistics tend to select complex models with overestimated numbers of components in mixture modeling. A full Bayesian approach is developed to analyze hidden Markov structural equation models with an unknown number of hidden states. An efficient and hybrid algorithm that combines the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm, the forward filtering and backward sampling scheme, and the Metropolis-Hastings algorithm is proposed to simultaneously select the number of hidden states and perform parameter estimation. The simulation study shows the satisfactory performance of the proposed method. Two real datasets collected from the UCLA Drug Abuse Research Center and National Longitudinal Survey of Youth are analyzed.
Bibliography Citation
Liu, Hefei and Xinyuan Song. "Bayesian Analysis of Hidden Markov Structural Equation Models with an Unknown Number of Hidden States." Econometrics and Statistics published online (21 May 2020): DOI: 10.1016/j.ecosta.2020.03.003.
2. Wang, Xiaoqing
Wu, Haotian
Feng, Xiangnan
Song, Xinyuan
Bayesian Two-level Model for Repeated Partially Ordered Responses: Application to Adolescent Smoking Behavior Analysis
Sociological Methods and Research published online (5 March 2019): DOI: 10.1177/0049124119826149.
Also: https://journals.sagepub.com/doi/full/10.1177/0049124119826149
Cohort(s): NLSY97
Publisher: Sage Publications
Keyword(s): Adolescent Behavior; Bayesian; Monte Carlo; Smoking (see Cigarette Use)

Permission to reprint the abstract has not been received from the publisher.

Given the questionnaire design and the nature of the problem, partially ordered data that are neither completely ordered nor completely unordered are frequently encountered in social, behavioral, and medical studies. However, early developments in partially ordered data analysis are very limited and restricted only to cross-sectional data. In this study, we propose a Bayesian two-level regression model for analyzing repeated partially ordered responses in longitudinal data. The first-level model is defined for partially ordered observations of interest that are taken at each time point nested within individuals, while the second-level model is defined for individuals to assess the effects of their characteristics on the first-level model. A full Bayesian approach with the Markov chain Monte Carlo algorithm is developed for statistical inference. Simulation studies demonstrate the satisfactory performance of the developed methodology. The methodology is then applied to a longitudinal study on adolescent smoking behavior.
Bibliography Citation
Wang, Xiaoqing, Haotian Wu, Xiangnan Feng and Xinyuan Song. "Bayesian Two-level Model for Repeated Partially Ordered Responses: Application to Adolescent Smoking Behavior Analysis." Sociological Methods and Research published online (5 March 2019): DOI: 10.1177/0049124119826149.