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

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).

Notes

¹Only the results for four measurement occasions are reported. The results under other conditions are similar and are omitted for the sake of saving space. Those results are available on request or can be found at http://webstats.psychstat.org/models/1gcm/robdiag/MBR.supp.zip

²The posterior credible interval in Bayesian analysis, also called credible interval or Bayesian confidence interval, is analogical to the frequentist confidence interval.