Diagnostics of Robust Growth Curve Modeling Using Student's t Distribution

Multivariate Behavioral Research
Xin Tong, Zhiyong Zhang

Abstract

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).

References

Jul 25, 2009·Statistics in Medicine·David LunnNicky Best
Jul 1, 2007·Learning and Individual Differences·Zhiyong ZhangElliot M Tucker-Drob
Jan 29, 2010·Multivariate Behavioral Research·Jiyun Zu, Ke-Hai Yuan

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Citations

May 29, 2015·Behavior Research Methods·Zhiyong Zhang
May 1, 2014·Multivariate Behavioral Research·Xin Tong, Zhiyong Zhang
Nov 22, 2017·Multivariate Behavioral Research·Xin Tong, Zhiyong Zhang
Aug 15, 2018·Behavior Research Methods·Jessica A M MazenLaura K Taylor
Aug 28, 2020·Multivariate Behavioral Research·Jessica A M Mazen, Xin Tong
Jan 1, 2017·Structural Equation Modeling : a Multidisciplinary Journal·Elizabeth M PlanalpLijuan Wang
Jan 30, 2021·The British Journal of Mathematical and Statistical Psychology·Ke-Hai Yuan, Brenna Gomer
Sep 15, 2020·The British Journal of Mathematical and Statistical Psychology·Xin TongJianhui Zhou

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