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Author: Zhang, Zhiyong
Resulting in 8 citations.
1. Lu, Zhenqiu Laura
Zhang, Zhiyong
Robust Growth Mixture Models with Non-ignorable Missingness: Models, Estimation, Selection, and Application
Computational Statistics and Data Analysis 71 (March 2014): 220-240.
Also: http://www.sciencedirect.com/science/article/pii/S0167947313002818
Cohort(s): NLSY97
Publisher: Elsevier
Keyword(s): Bayesian; Missing Data/Imputation; Modeling; Peabody Individual Achievement Test (PIAT- Math); Statistical Analysis

Challenges in the analyses of growth mixture models include missing data, outliers, estimation, and model selection. Four non-ignorable missingness models to recover the information due to missing data, and three robust models to reduce the effect of non-normality are proposed. A full Bayesian method is implemented by means of data augmentation algorithm and Gibbs sampling procedure. Model selection criteria are also proposed in the Bayesian context. Simulation studies are then conducted to evaluate the performances of the models, the Bayesian estimation method, and selection criteria under different situations. The application of the models is demonstrated through the analysis of education data on children’s mathematical ability development. The models can be widely applied to longitudinal analyses in medical, psychological, educational, and social research.
Bibliography Citation
Lu, Zhenqiu Laura and Zhiyong Zhang. "Robust Growth Mixture Models with Non-ignorable Missingness: Models, Estimation, Selection, and Application." Computational Statistics and Data Analysis 71 (March 2014): 220-240.
2. Lu, Zhenqiu Laura
Zhang, Zhiyong
Lubke, Gitta H.
Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data
Multivariate Behavioral Research 46,4 (2011): 567-597.
Also: http://www.tandfonline.com/doi/abs/10.1080/00273171.2011.589261
Cohort(s): NLSY97
Publisher: Taylor & Francis
Keyword(s): Bayesian; Missing Data/Imputation; Modeling, Growth Curve/Latent Trajectory Analysis

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.
Bibliography Citation
Lu, Zhenqiu Laura, Zhiyong Zhang and Gitta H. Lubke. "Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data." Multivariate Behavioral Research 46,4 (2011): 567-597.
3. 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.
4. 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.
5. 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.
6. Zhang, Zhiyong
Bayesian Analysis of Longitudinal Data Using Growth Curve Models
Ph.D. Dissertation, University of Virginia, Department of Psychology, 2008
Cohort(s): Children of the NLSY79
Publisher: ProQuest Dissertations & Theses (PQDT)
Keyword(s): Bayesian; Behavior Problems Index (BPI); Growth Curves; Modeling, Growth Curve/Latent Trajectory Analysis; Peabody Individual Achievement Test (PIAT- Math); Peabody Individual Achievement Test (PIAT- Reading); Variables, Independent - Covariate

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

Generally, at least two features are needed to characterize a growth process fully at any time point: the level of growth and the rate of growth. The level of growth represents the current status of a process at a given time point and can be viewed as a static measure of that process. The rate of growth represents how fast the level of the process is changing at that time point and can be viewed as a dynamic measure of the process. The widely used growth curve models usually focus on the analysis of the level of growth. However, techniques for analysis of rates of growth are still relatively rare. Because of the significance of rates of growth in understanding dynamic processes, a stronger and more versatile approach is proposed to model them by constructing growth rate models. The concepts of growth processes and current analytical techniques are first reviewed and both the simple rate of growth and the compound rate of growth are defined. Then, different models are developed to analyze rates of growth. Growth rate models are constructed to analyze simple rates of growth and random coefficient models are developed to analyze compound rates of growth. The proposed models are applied to analyze an empirical data set--the National Longitudinal Study of Youth (NLSY)--consisting of children's mathematics performance data and covariates of gender and behavioral problems (BPI).

Individual differences are found in both simple and compound rates of growth. BPI and gender have different relationship with simple rates of growth at different ages. BPI is also found to be negatively related to compound rates of growth. Finally, a systematic simulation study is conducted to validate the results from the analysis of the NLSY data and to investigate the performance of two main models, the quadratic growth rate model and the random coefficient latent difference score model. The simulation results support the validity of the results from the empirical data analysis. It is further found that the parameter estimates for both models are unbiased and the standard error estimates are consistent.

Bibliography Citation
Zhang, Zhiyong. Bayesian Analysis of Longitudinal Data Using Growth Curve Models. Ph.D. Dissertation, University of Virginia, Department of Psychology, 2008.
7. Zhang, Zhiyong
Hamagami, Fumiaki
Wang, Lijuan
Nesselroade, John R.
Grimm, Kevin J.
Bayesian Analysis of Longitudinal Data Using Growth Curve Models
International Journal of Behavioral Development 31,4 (July 2007): 374-383.
Also: http://jbd.sagepub.com/content/31/4/374.abstract
Cohort(s): Children of the NLSY79
Publisher: Taylor & Francis
Keyword(s): Bayesian; Growth Curves; Methods/Methodology; Modeling, Growth Curve/Latent Trajectory Analysis; Peabody Individual Achievement Test (PIAT- Reading); Statistical Analysis

Bayesian methods for analyzing longitudinal data in social and behavioral research are recommended for their ability to incorporate prior information in estimating simple and complex models. We first summarize the basics of Bayesian methods before presenting an empirical example in which we fit a latent basis growth curve model to achievement data from the National Longitudinal Survey of Youth. This step-by-step example illustrates how to analyze data using both noninformative and informative priors. The results show that in addition to being an alternative to the maximum likelihood estimation (MLE) method, Bayesian methods also have unique strengths, such as the systematic incorporation of prior information from previous studies. These methods are more plausible ways to analyze small sample data compared with the MLE method.

Data
Data in this example are two subsets from the National Longitudinal Survey of Youth (NLSY).2 The first subset includes repeated measurements of N = 173 children. At the first measurement in 1986, the children were about 6–7 years of age. The same children were then repeatedly measured at 2-year intervals for three additional measurement occasions (1988, 1990, and 1992). Missing data existed for some of the children. The second subset includes repeated measurements of N = 34 children. At their first measurement in 1992, the children were also about 6–7 years of age. The same children were also measured again at an approximate 2-year interval for another three times in years 1994, 1996, and 1998. Missing data also existed for several of the children. The children from both data sets were tested using the Peabody Individual Achievement Test (PIAT) Reading Recognition subtest that measured word recognition and pronunciation ability. The total score for this subtest ranged in value from 0 to 84. In the present study, this score was rescaled by dividing by 10. [ABSTRACT FROM AUTHOR]

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Bibliography Citation
Zhang, Zhiyong, Fumiaki Hamagami, Lijuan Wang, John R. Nesselroade and Kevin J. Grimm. "Bayesian Analysis of Longitudinal Data Using Growth Curve Models." International Journal of Behavioral Development 31,4 (July 2007): 374-383.
8. Zhang, Zhiyong
McArdle, John J.
Nesselroade, John R.
Growth Rate Models: Emphasizing Growth Rate Analysis through Growth Curve Modeling
Journal of Applied Statistics 39,6 (June 2012): 1241-1262.
Also: http://www.tandfonline.com/doi/abs/10.1080/02664763.2011.644528
Cohort(s): Children of the NLSY79
Publisher: Taylor & Francis Group
Keyword(s): Behavior Problems Index (BPI); Gender Differences; Modeling, Growth Curve/Latent Trajectory Analysis; Peabody Individual Achievement Test (PIAT- Math); Test Scores/Test theory/IRT

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

To emphasize growth rate analysis, we develop a general method to reparametrize growth curve models to analyze rates of growth for a variety of growth trajectories, such as quadratic and exponential growth. The resulting growth rate models are shown to be related to rotations of growth curves. Estimated conveniently through growth curve modeling techniques, growth rate models have advantages above and beyond traditional growth curve models. The proposed growth rate models are used to analyze longitudinal data from the National Longitudinal Study of Youth (NLSY) on children's mathematics performance scores including covariates of gender and behavioral problems (BPI). Individual differences are found in rates of growth from ages 6 to 11. Associations with BPI, gender, and their interaction to rates of growth are found to vary with age. Implications of the models and the findings are discussed.
Bibliography Citation
Zhang, Zhiyong, John J. McArdle and John R. Nesselroade. "Growth Rate Models: Emphasizing Growth Rate Analysis through Growth Curve Modeling." Journal of Applied Statistics 39,6 (June 2012): 1241-1262.