Detecting Individual Differences in Change: Methods and Comparisons

Structural Equation Modeling

Volumn 22, Issue 3, 2015, Pages 382-400

  Ke, Zijun ^a  

^a SUN YAT SEN UNIVERSITY   (China)

^b Peggy)   (United States)

Author keywords

constrained vs. unconstrained estimation; growth curve modeling; nonnormality; specific vs. generalized tests; variance tests

Indexed keywords

ERRORS;

CONSTRAINED ESTIMATION; CORRECTION APPROACHES; ESTIMATION PROCEDURES; GENERALIZED VARIANCE; GROWTH CURVE MODELS; INDIVIDUAL DIFFERENCES; MIXTURE DISTRIBUTIONS; NON-NORMALITY;

TESTING;

EID: 84930577612     PISSN: 10705511     EISSN: 15328007     Source Type: Journal    
DOI: 10.1080/10705511.2014.936096     Document Type: Article

References (40)

1. P.Baltes,, & J.R.Nesselroade, (1979). History and rationale of longitudinal research. In J.R.Nesselroade & P.B.Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 1–39). New York, NY: Academic Press.
2. D.J.Bauer, (2003). Estimating multilevel linear models as structural equation models. Journal of Educational and Behavioral Statistics, 28, 135–167.
3. D.J.Bauer, (2011). Evaluating individual differences in psychological processes. Current Directions in Psychological Science, 20, 115–118.
4. P.M.Bentler,, & K.-H.Yuan, (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181–197.
5. J.V.Bradley, (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144–152.
6. G.M.Fitzmaurice,, N.M.Laird,, & J.H.Ware, (2011). Applied longitudinal analysis (2nd ed.). New York, NY: Wiley.
7. K.J.Grimm,, A.P.Kuhl,, & Z.Zhang, (2013). Measurement models, estimation, and the study of change. Structural Equation Modeling, 20, 504–517.
8. G.R.Hancock,, & J.Choi, (2006). A vernacular for linear latent growth models. Structural Equation Modeling, 13, 352–377.
9. D.R.Hedeker,, & R.D.Gibbons, (2003). Applied longitudinal data analysis. New York, NY: Wiley-Interscience.
10. C.Hertzog,, & K.W.Schaie, (1986). Stability and change in adult intelligence: 1. Analysis of longitudinal covariance structures. Psychology and Aging, 1, 159–171.
11. C.Hertzog,, T.von Oertzen,, P.Ghisletta,, & U.Lindenberger, (2008). Evaluating the power of latent growth curve models to detect individual differences in change. Structural Equation Modeling, 15, 541–563.
12. D.M.LaHuis,, & M.W.Ferguson, (2009). The accuracy of significance tests for slope variance components in multilevel random coefficient models. Organizational Research Methods, 12, 435.
13. P.-W.Lei,, & Q.Wu, (2012). Estimation in structural equation modeling. In R.H.Hoyle (Ed.), Handbook of structural equation modeling (pp. 164–180). New York, NY: Guilford.
14. M.Lovden,, P.Ghisletta,, & U.Lindenberger, (2004). Cognition in the Berlin aging study (BASE): The first 10 years. Aging, Neuropsychology, and Cognition, 11, 104–133.
15. R.C.MacCallum,, C.Kim,, W.B.Malarkey,, & J.K.Kiecolt-Glaser, (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215–253.
16. J.R.Magnus,, & H.Neudecker, (1999). Matrix differential calculus with applications in statistics and econometrics (2nd ed.). New York, NY: Wiley.
17. J.J.McArdle, (2009). Latent variable modeling of longitudinal data. Annual Review of Psychology, 60, 577–605.
18. J.J.McArdle, (2013). A theory of longitudinal data analysis. Washington, DC: APA Books.
19. W.Meredith,, & J.Tisak, (1990). Latent curve analysis. Psychometrika, 55, 107–122.
20. T.Micceri, (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166.
21. J.Navitt,, & G.R.Hancock, (2004). Evaluating small sample approaches for model test statistic in structural equation modeling. Multivariate Behavioral Research, 39, 439–478.
22. P.Rast,, & S.M.Hofer, (2014). Longitudinal design considerations to optimize power to detect variances and covariances among rates of change: Simulation results based on actual longitudinal studies. Psychological Methods, 19, 133–154.
23. S.Raudenbush,, & A.Bryk, (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage.
24. Y.Rosseel, (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. Retrieved from http://www.jstatsoft.org/v48/i02
25. A.Satorra, (2000). Scaled and adjusted restricted tests in multi-sample analysis of moment structures. In D.Heijmans & A.S.D.S.G.Pollock (Eds.), Innovations in multivariate statistical analysis: A festschrift for Heinz Neudecker (pp. 233–247). Dordrecht, The Netherlands: Kluwer Academic.
26. A.Satorra,, & P.M.Bentler, (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66, 507–514.
27. A.Satorra,, & P.M.Bentler, (2010). Ensuring positiveness of the scaled difference chi-square test statistic. Psychometrika, 75, 243–248.
28. V.Savalei,, & S.Kolenikov, (2008). Constrained versus unconstrained estimation in structural equation modeling. Psychological Methods, 13, 150–170.
29. S.G.Self,, & K.-Y.Liang, (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of American Statistical Association, 82, 605–610.
30. J.D.Singer,, & J.B.Willett, (2003). Applied longitudinal data analysis modeling change and event occurrence. New York, NY: Oxford University Press.
31. R.D.Stoel,, F.G.Garre,, C.Dolan,, & G.van den Wittenboer,. (2006). On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods, 4, 439–455.
32. D.Stram,, & J.-W.Lee, (1994). Variance components testing in the longitudinal mixed effects model. Biometrics, 50, 1171–1177.
33. G.Verbeke,, & G.Molenberghs, (2009). Linear mixed models for longitudinal data (3rd ed.). New York, NY: Springer Series in Statistics.
34. T.von Oertzen, (2010). Power equivalence in structural equation modeling. British Journal of Mathematical and Statistical Psychology, 63, 257–272.
35. T.von Oertzen,, & A.M.Brandmaier, (2012). Optimal study design with identical power: An application of power equivalence to latent growth curve model. Psychology and Aging, 28, 414–428.
36. L.Wang,, & J.J.McArdle, (2008). A simulation study comparison of Bayesian estimation with conventional methods for estimating unknown change points. Structural Equation Modeling, 15, 52–74.
37. J.B.Willett, (1989). Some results on reliability for the longitudinal measurement of change: Implications for the design of studies of individual growth. Educational & Psychological Measurement, 49, 587–602.
38. K.-H.Yuan, (2005). Fit indices versus test statistics. Multivariate Behavioral Research, 40, 115–148.
39. K.-H.Yuan,, & P.M.Bentler, (1998). Normal theory based test statistics in structural equation modeling. British Journal of Mathematical and Statistical Psychology, 51, 289–309.
40. K.-H.Yuan,, & K.Hayashi, (2006). Standard errors in covariance structure models: Asymptotics versus bootstrap. British Journal of Mathematical and Statistical Psychology, 59, 397–417.