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Author: Tong, Xin
Resulting in 4 citations.
1. Tong, Xin
Zhang, Zhiyong
Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution
Multivariate Behavioral Research 47,4 (2012): 493-518.
Also: http://www.tandfonline.com/doi/full/10.1080/00273171.2012.692614
Cohort(s): NLSY97
Publisher: Taylor & Francis
Keyword(s): Modeling, Growth Curve/Latent Trajectory Analysis; Peabody Individual Achievement Test (PIAT- Math)

Growth curve models with different types of distributions of random effects and of intraindividual measurement errors for robust analysis are compared. After demonstrating the influence of distribution specification on parameter estimation, 3 methods for diagnosing the distributions for both random effects and intraindividual measurement errors are proposed and evaluated. The methods include (a) distribution checking based on individual growth curve analysis; (b) distribution comparison based on Deviance Information Criterion, and (c) post hoc checking of degrees of freedom estimates for t distributions. The performance of the methods is compared through simulation studies. When the sample size is reasonably large, the method of post hoc checking of degrees of freedom estimates works best. A web interface is developed to ease the use of the 3 methods. Application of the 3 methods is illustrated through growth curve analysis of mathematical ability development using data on the Peabody Individual Achievement Test Mathematics assessment from the National Longitudinal Survey of Youth 1997 Cohort (Bureau of Labor Statistics, U.S. Department of Labor, 2005).
Bibliography Citation
Tong, Xin and Zhiyong Zhang. "Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution." Multivariate Behavioral Research 47,4 (2012): 493-518.
2. Tong, Xin
Zhang, Zhiyong
Outlying Observation Diagnostics in Growth Curve Modeling
Multivariate Behavioral Research 52,6 (2017): 768-788.
Also: http://www.tandfonline.com/doi/full/10.1080/00273171.2017.1374824
Cohort(s): NLSY97
Publisher: Taylor & Francis
Keyword(s): Modeling, Growth Curve/Latent Trajectory Analysis; Monte Carlo; Peabody Individual Achievement Test (PIAT- Math); Statistical Analysis

Growth curve models are widely used for investigating growth and change phenomena. Many studies in social and behavioral sciences have demonstrated that data without any outlying observation are rather an exception, especially for data collected longitudinally. Ignoring the existence of outlying observations may lead to inaccurate or even incorrect statistical inferences. Therefore, it is crucial to identify outlying observations in growth curve modeling. This study comparatively evaluates six methods in outlying observation diagnostics through a Monte Carlo simulation study on a linear growth curve model, by varying factors of sample size, number of measurement occasions, as well as proportion, geometry, and type of outlying observations. It is suggested that the greatest chance of success in detecting outlying observations comes from use of multiple methods, comparing their results and making a decision based on research purposes. A real data analysis example is also provided to illustrate the application of the six outlying observation diagnostic methods.
Bibliography Citation
Tong, Xin and Zhiyong Zhang. "Outlying Observation Diagnostics in Growth Curve Modeling." Multivariate Behavioral Research 52,6 (2017): 768-788.
3. Tong, Xin
Zhang, Zhiyong
Robust Bayesian Approaches in Growth Curve Modeling: Using Student's t Distributions versus a Semiparametric Method
Structural Equation Modeling: A Multidisciplinary Journal published online (11 November 2019): DOI: 10.1080/10705511.2019.1683014.
Also: https://www.tandfonline.com/doi/full/10.1080/10705511.2019.1683014
Cohort(s): NLSY97
Publisher: Lawrence Erlbaum Associates ==> Taylor & Francis
Keyword(s): Bayesian; Modeling, Growth Curve/Latent Trajectory Analysis; Monte Carlo; Peabody Individual Achievement Test (PIAT- Math)

Permission to reprint the abstract has been denied by the publisher.

Bibliography Citation
Tong, Xin and Zhiyong Zhang. "Robust Bayesian Approaches in Growth Curve Modeling: Using Student's t Distributions versus a Semiparametric Method." Structural Equation Modeling: A Multidisciplinary Journal published online (11 November 2019): DOI: 10.1080/10705511.2019.1683014.
4. Wang, Lijuan
Zhang, Zhiyong
Tong, Xin
Mediation Analysis with Missing Data through Multiple Imputation and Bootstrap
Working Paper, Department of Psychology, University of Notre Dame, January 2014
Cohort(s): Children of the NLSY79
Publisher: Department of Psychology, University of Notre Dame
Keyword(s): Behavior Problems Index (BPI); Home Observation for Measurement of Environment (HOME); Missing Data/Imputation; Mothers, Education; Peabody Individual Achievement Test (PIAT- Math); Peabody Individual Achievement Test (PIAT- Reading); Statistical Analysis

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

A method using multiple imputation and bootstrap for dealing with miss- ing data in mediation analysis is introduced and implemented in SAS. Through simulation studies, it is shown that the method performs well for both MCAR and MAR data without and with auxiliary variables. It is also shown that the method works equally well for MNAR data if auxiliary vari- ables related to missingness are included. The application of the method is demonstrated through the analysis of a subset of data from the National Longitudinal Survey of Youth.
Bibliography Citation
Wang, Lijuan, Zhiyong Zhang and Xin Tong. "Mediation Analysis with Missing Data through Multiple Imputation and Bootstrap." Working Paper, Department of Psychology, University of Notre Dame, January 2014.