Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

REFERENCES

• Baltes , P. B. and Nesselroade , J. R. 1979 . “ History and rationale of longitudinal research. ” . In Longitudinal research in the study of behavior and development Edited by: Nesselroade , J. R. and Baltes , P. B. 1 – 39 . New York : Academic Press .
   Google Scholar
• Bauer , D. J. and Curran , P. J. 2003 . Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes . Psychological Methods , 8 : 338 – 363 .
   PubMed Web of Science ®Google Scholar
• Boker , S. , Neale , M. , Maes , H. , Wilde , M. , Spiegel , M. Brick , T. “ OpenMx: An open source extended structural equation modeling framework ” . In Psychometrika (in press)
   Google Scholar
• Browne , M. W. 1993 . “ Structured latent curve models ” . In Multivariate analysis: Future directions Edited by: Cuadras , C. M. and Rao , C. R. Vol. 2 , 171 – 198 . Amsterdam : North-Holland .
   Google Scholar
• Browne , M. W. and du Toit , S. H. C. 1991 . “ Models for learning data. ” . In Best methods for the analysis of change Edited by: Collins , L. and Horn , J. L. 47 – 68 . Washington, DC : American Psychological Association .
   Google Scholar
• Burchinal , M. and Appelbaum , M. 1991 . Estimating individual developmental functions: Methods and their assumptions . Child Development , 62 : 23 – 43 .
   Web of Science ®Google Scholar
• Grimm , K. J. , McArdle , J. J. and Hamagami , F. 2007 . “ Nonlinear growth mixture models in research on cognitive aging. ” . In Longitudinal models in the behavioral and related sciences Edited by: van Montfort , K. , Oud , J. and Satorra , A. 267 – 295 . Mahwah, NJ : Erlbaum .
   Google Scholar
• Grimm , K. J. and Ram , N. 2009 . Nonlinear growth models in Mplus and SAS . Structural Equation Modeling , 16 : 676 – 701 .
   PubMed Web of Science ®Google Scholar
• Grimm , K. J. and Ram , N. “ Latent growth curves in the SEM framework ” . In Handbook of developmental research methods Edited by: Laursen , B. , Little , T. and Card , N. New York : Guilford. . (in press)
   Google Scholar
• Grimm , K. J. , Ram , N. and Hamagami , F. “ Nonlinear growth curves in developmental research ” . In Child Development (in press)
   Google Scholar
• Harring , J. R. 2005 . Nonlinear mixed effects mixture model: A model for clustering nonlinear longitudinal profiles. Unpublished doctoral dissertation, University of Minnesota, Minneapolis
   Google Scholar
• Harring , J. R. , Cudeck , R. and du Toit , S. H. C. 2006 . Fitting partially nonlinear random coefficient models as SEMs . Multivariate Behavioral Research , 41 : 579 – 596 .
   PubMed Web of Science ®Google Scholar
• Kaplan , D. 2002 . Methodological advances in the analysis of individual growth with relevance to education policy . Peabody Journal of Education , 77 : 189 – 215 .
   Google Scholar
• Kelley , K. 2005 . Estimating nonlinear change models in heterogeneous populations when class membership is unknown: Defining and developing the latent classification differential change model. Unpublished doctoral dissertation, University of Notre Dame, South Bend, IN
   Google Scholar
• Kelley , K. 2008 . Nonlinear change models in populations with unobserved heterogeneity . Methodology , 4 : 97 – 112 .
   Web of Science ®Google Scholar
• McArdle , J. J. and Nesselroade , J. R. 2003 . “ Growth curve analysis in contemporary psychological research. ” . In Comprehensive handbook of psychology: Vol. 2. Research methods in psychology Edited by: Shinka , J. and Velicer , W. 447 – 480 . New York : Wiley .
   Google Scholar
• McLachlan , G. J. and Peel , D. 2000 . Finite mixture models New York : Wiley .
   Google Scholar
• Meredith , W. and Tisak , J. 1990 . Latent curve analysis . Psychometrika , 55 : 107 – 122 .
   Web of Science ®Google Scholar
• Morrison , F. J. , Smith , L. and Dow-Ehrensberger , M. 1995 . Education and cognitive development: A natural experiment . Developmental Psychology , 31 : 789 – 799 .
   Web of Science ®Google Scholar
• Muthén , B. O. 2003 . Statistical and substantive checking in growth mixture modeling . Psychological Methods , 8 : 369 – 377 .
   PubMed Web of Science ®Google Scholar
• Muthén , B. O. , Khoo , S. T. , Francis , D. and Boscardin , K. C. 2003 . “ Analysis of reading skills development from kindergarten through first grade: An application of growth mixture modeling to sequential processes. ” . In Multilevel modeling: Methodological advances, issues, and applications Edited by: Reise , S. R. and Duan , N. 71 – 89 . Mahwah, NJ : Erlbaum .
   Google Scholar
• Muthén , B. O. and Muthén , L. K. 2000 . Integrating person-centered and variable-centered analysis: Growth mixture modeling with latent trajectory classes . Alcoholism: Clinical and Experimental Research , 24 : 882 – 891 .
   PubMed Web of Science ®Google Scholar
• Muthén , B. O. and Shedden , K. 1999 . Finite mixture modeling with mixture outcomes using the EM algorithm . Biometrics , 55 : 463 – 469 .
   PubMed Web of Science ®Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998–2007 . Mplus user's guide, , 6th ed. Los Angeles: Author
   Google Scholar
• Nylund , K. L. , Asparouhov , T. and Muthén , B. 2007 . Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study . Structural Equation Modeling , 14 : 535 – 569 .
   Web of Science ®Google Scholar
• Pianta , R. , Belsky , J. , Vandergrift , N. , Houts , R. , Morrison , F. and NICHD , ECCRN . 2008 . Classroom effects on children's achievement trajectories in elementary school . American Educational Research Journal , 45 : 365 – 397 .
   Web of Science ®Google Scholar
• R Development Core Team. 2009 . R: A language and environment for statistical computing Vienna : R Foundation for Statistical Computing. . Available from http://www.R-project.org
   Google Scholar
• Ram , N. and Grimm , K. J. 2009 . Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups . International Journal of Behavioral Development , 33 : 565 – 576 .
   PubMed Web of Science ®Google Scholar
• Willett , J. B. and Sayer , A. G. 1994 . Using covariance structure analysis to detect correlates and predictors of individual change over time . Psychological Bulletin , 116 : 363 – 381 .
   Web of Science ®Google Scholar
• Wohlwill , J. F. 1973 . The study of behavioral development. New York : Academic Press .
   Google Scholar