Bayesian Inference and Application of Robust Growth Curve Models Using Student's "t" Distribution

Autor/inn/en	Zhang, Zhiyong; Lai, Keke; Lu, Zhenqiu; Tong, Xin
Titel	Bayesian Inference and Application of Robust Growth Curve Models Using Student's "t" Distribution
Quelle	In: Structural Equation Modeling: A Multidisciplinary Journal, 20 (2013) 1, S.47-78 (32 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1070-5511
DOI	10.1080/10705511.2013.742382
Schlagwörter	Structural Equation Models; Bayesian Statistics; Statistical Inference; Statistical Distributions; Computation; Robustness (Statistics); Mathematics Tests; Mathematics Achievement; Achievement Tests; Grade 7; Grade 8; Grade 9; Grade 10; Grade 11; Secondary School Students; Simulation; Maximum Likelihood Statistics; National Longitudinal Survey of Youth; Peabody Individual Achievement Test + Suchen Sie Ihr Suchwort? Inferential statistics; Schließende Statistik; Wahrscheinlichkeitsverteilung; Widerstandsfähigkeit; Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Achievement test; Achievement; Testing; Test; Tests; Leistungsbeurteilung; Leistungsüberprüfung; Leistung; Testdurchführung; Testen; School year 07; 7. Schuljahr; Schuljahr 07; School year 08; 8. Schuljahr; Schuljahr 08; School year 09; 9. Schuljahr; Schuljahr 09; School year 11; 11. Schuljahr; Schuljahr 11; Sekundarschüler; Simulation program; Simulationsprogramm
Abstract	Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian methods utilizing data augmentation and Gibbs sampling algorithms. The analysis of mathematical development data shows that the robust latent basis growth curve model better describes the mathematical growth trajectory than the corresponding normal growth curve model and can reveal the individual differences in mathematical development. Simulation studies further confirm that the robust growth curve models significantly outperform the normal growth curve models for both heavy-tailed "t" data and normal data with outliers but lose only slight efficiency for normal data. It appears convincing to replace the normal distribution with the "t" distribution for growth curve analysis. Three information criteria are evaluated for model selection. Online software is also provided for conducting robust analysis discussed in this study. (Contains 11 tables, 2 figures, and 3 footnotes.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10