Power of Latent Growth Curve Models to Detect Piecewise Linear Trajectories

REFERENCES

• Beauchaine, T., & Beauchaine, R. (2002). A comparison of maximum covariance and k-means cluster analysis in classifying cases into known taxon groups. Psychological Methods, 7, 245–261.
   PubMed Web of Science ®Google Scholar
• Blozis, S. A. (2007). On fitting nonlinear latent curve models to multiple variables measured longitudinally. Structural Equation Modeling, 14, 179–201.
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
   Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. New York, NY: Wiley.
   Google Scholar
• Browne, M. W., & du Toit, S. H. C. (1991). Models for learning data. In L. Collins & J. L. Horn (Eds.), Best methods for the analysis of change (pp. 47–68). Washington, DC: APA.
   Google Scholar
• Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear model: Applications and data analysis methods. Newbury Park, CA: Sage.
   Google Scholar
• Cheong, J. (2011). Accuracy of estimates and statistical power for testing mediation in latent growth curve modeling. Structural Equation Modeling, 18, 195–211.
   PubMed Web of Science ®Google Scholar
• Cheong, J., MacKinnon, D. P., & Khoo, S. T. (2003). Investigation of meditational processes using parallel process latent growth curve modeling. Structural Equation Modeling, 10, 238–262.
   PubMed Web of Science ®Google Scholar
• Chou, C.-P, Bentler, P. M., & Pentz, M. A. (1998). Comparisons of two statistical approaches to study growth curves: The multilevel model and the latent curve analysis. Structural Equation Modeling, 5, 247–266.
   Web of Science ®Google Scholar
• Cudeck, R. & Harring, J. R. (2007). Analysis of nonlinear patterns of change with random coefficient models. Annual Review of Psychology, 58, 615–637.
   PubMed Web of Science ®Google Scholar
• Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7, 41–63.
   PubMed Web of Science ®Google Scholar
• Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529–569.
   PubMed Web of Science ®Google Scholar
• DasGupta, A. (2008). Asymptotic theory of statistics and probability. New York, NY: Springer.
   Google Scholar
• Duncan, T. E., Duncan, S. C., Strycker, L. A., & Li, F. (2002). A latent variable framework for power estimation within intervention contexts. Journal of Psychopathology & Behavioral Assessment, 24, 1–12.
   Web of Science ®Google Scholar
• Eccles, J. S., Midgley, C., Wigfield, A., Buchanan, C. M., Reuman, D., Flanagan, C., & Mac Iver, D. (1993). Development during adolescence: The impact stage–environment fit on young adolescents’ experiences in schools and in families. American Psychologist, 48, 90–101.
   PubMed Web of Science ®Google Scholar
• Fan, X. (2003). Power of latent growth modeling for detecting group differences in linear growth trajectory parameters. Structural Equation Modeling, 10, 380–400.
   Web of Science ®Google Scholar
• Fan, X., & Fan, X. (2005). Power of latent growth modeling for detecting linear growth: Number of measurements and comparison with other analytical approaches. The Journal of Experimental Education, 73, 121–139.
   Web of Science ®Google Scholar
• Ferron, J., Dailey, R., & Yi, Q. (2002). Effects of misspecifying the first-level error structure in two-level models of change. Multivariate Behavioral Research, 37, 379–403.
   PubMed Web of Science ®Google Scholar
• Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling, 15, 513–533.
   Web of Science ®Google Scholar
• Grimm, K. J., Ram, N., & Hamagami, F. (2011). Nonlinear growth curves in developmental research. Child Development, 82, 1357–1371.
   PubMed Web of Science ®Google Scholar
• Hamaker, E. L., Dolan, C. V., & Molenaar, P. C. M. (2005). Statistical modeling of the individual: Rationale and application of multivariate stationary time series analyses. Multivariate Behavioral Research, 40, 207–233.
   PubMed Web of Science ®Google Scholar
• Hertzog, C., Lindenberger, U., Ghisletta, P., & von Oertzen, T. (2006). On the power of multivariate latent growth curve models to detect correlated change. Psychological Methods, 11, 244–252.
   PubMed Web of Science ®Google Scholar
• Hertzog, C., von Oertzen, T., Ghisletta, P., & Lindenberger, U. (2008). Evaluating the power of latent growth curve models to detect individual differences in change. Structural Equation Modeling, 15, 541–563.
   Web of Science ®Google Scholar
• Jones, C. J., & Meredith, W. (2000). Developmental paths of psychological health from early adolescence to later adulthood. Psychology and Aging, 15, 351–360.
   PubMed Web of Science ®Google Scholar
• Kwok, O., Luo, W., & West, S. G. (2010). Using modification indexes to detect turning points in longitudinal data: A Monte Carlo study. Structural Equation Modeling, 17, 216–240.
   Web of Science ®Google Scholar
• Kwok, O.-M., West, S. G., & Green, S. B. (2007). The impact of misspecifying the within-subject covariance structure in multiwave longitudinal multilevel models: A Monte Carlo study. Multivariate Behavioral Research, 42, 557–592.
   Web of Science ®Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.
   Web of Science ®Google Scholar
• Morin, A. J. S., Maïano, C., Nagengast, B., Marsh, H. W., Morizot, J., & Janosz, M. (2011). Growth mixture modeling of adolescents trajectories of anxiety across adolescence: The impact of untested invariance assumptions on substantive interpretations. Structural Equation Modeling, 18, 613–648.
   Web of Science ®Google Scholar
• Muthén, B. O., & Curran, P. (1997). General growth modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2, 371–402.
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (2011). Mplus user’s guide (6th ed). Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Ram, N., & Grimm, K. J. (2007). Using simple and complex growth models to articulate developmental change: Matching theory to method. International Journal of Behavioral Development, 31, 303–316.
   Web of Science ®Google Scholar
• Shadish, W. R., & Cook, T. D. (2009). The renaissance of field experimentation in evaluating interventions. Annual Review of Psychology, 60, 607–629.
   PubMed Web of Science ®Google Scholar
• Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY: Oxford University Press.
   Google Scholar
• Sun, R., & Willson, V. L. (2009). Evaluating intercept–slope interactions in latent growth modeling. Structural Equation Modeling, 16, 226–244.
   Web of Science ®Google Scholar
• Tofighi, D., & Enders, C. K. (2007). Identifying the correct number of classes in growth mixture models. In G. R. Hancock (Ed.), Mixture models in latent variable research (pp. 317–341). Greenwich, CT: Information Age.
   Google Scholar
• Voelkle, M. C. (2008). Reconsidering the use of autoregressive latent trajectory (ALT) models. Multivariate Behavioral Research, 43, 564–591.
   PubMed Web of Science ®Google Scholar
• Zhang, Z., & Wang, L. (2009). Statistical power analysis for growth curve models using SAS. Behavior Research Methods, 41, 1083–1094.
   PubMed Web of Science ®Google Scholar