The Impact and Interpretation of Modeling Residual Noninvariance in Growth Mixture Models

References

• Asparouhov, T., & Muthén, B. (2014). Structural equation models and mixture models with continuous non-normal skewed distributions. Mplus Web Notes: No. 19.
   Google Scholar
• Bailey, K. D. (1994). Typologies and taxonomies: An introduction to classification techniques (Vol. 102). Thousand Oaks, CA: Sage.
   Google Scholar
• Bauer, D. J., & Curran, P. J. (2003). Distributional assumptions of growth mixture models: Implications for overextraction of latent trajectory classes. Psychological Methods, 8(3), 338–363. doi:10.1037/1082-989X.8.3.338
   PubMed Web of Science ®Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley-Interscience.
   Google Scholar
• Brown, C. H., Wang, W., Kellam, S. G., Muthén, B. O., Petras, H., Toyinbo, P., … Group, M. (2008). Methods for testing theory and evaluating impact in randomized field trials: Intent-to-treat analyses for integrating the perspectives of person, place, and time. Drug and Alcohol Dependence, 95, S74–S104. doi:10.1016/j.drugalcdep.2007.11.013
   PubMed Web of Science ®Google Scholar
• Chafouleas, S. (2011). Direct behavior rating: a review of the issues and research in its development. Education and treatment of children, 34, 575–591.
   Google Scholar
• Chen, Q., Kwok, O., Luo, W., & Willson, V. L. (2010). The impact of ignoring a level of nesting structure in multilevel growth mixture models: A Monte Carlo study. Structural Equation Modeling: A Multidisciplinary Journal, 17(4), 570–589. doi:10.1080/10705511.2010.510046
   Web of Science ®Google Scholar
• Clark, S. L., & Muthén, B. (2009). Relating latent class analysis results to variables not included in the analysis. Retrieved from https://www.statmodel.com/download/relatinglca.pdf
   Google Scholar
• Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. Mason, OH: Cengage Learning.
   Google Scholar
• Diallo, T. M. O., Morin, A. J. S., & Lu, H. (2016). Impact of misspecifications of the latent variance-covariance and residual matrices on the class enumeration accuracy of growth mixture models. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 507–531. doi:10.1080/10705511.2016.1169188
   Web of Science ®Google Scholar
• Distefano, C., & Kamphaus, R. W. (2006). Investigating subtypes of child development: A comparison of cluster analysis and latent class cluster analysis in typology creation. Educational and Psychological Measurement, 66(3), 778–794. doi:10.1177/0013164405284033
   Google Scholar
• DiStefano, C., & Kamphaus, R. W. (2008). Latent growth curve modeling of child behavior in elementary school. Research in the Schools, 15(1), 27–37.
   Google Scholar
• Dowdy, E., Nylund-Gibson, K., Felix, E. D., Morovati, D., Carnazzo, K. W., & Dever, B. V. (2014). Long-term stability of screening for behavioral and emotional risk. Educational and Psychological Measurement, 74(3), 453–472. doi:10.1177/0013164413513460
   Web of Science ®Google Scholar
• Enders, C. K., & Tofighi, D. (2008). The impact of misspecifying class-specific residual variances in growth mixture models. Structural Equation Modeling: A Multidisciplinary Journal, 15(1), 75–95. doi:10.1080/10705510701758281
   Web of Science ®Google Scholar
• Finch, W. H., & French, B. F. (2014). Multilevel latent class analysis: Parametric and nonparametric models. Journal of Experimental Education, 82(3), 307–333. doi:10.1080/00220973.2013.813361
   Web of Science ®Google Scholar
• Fuchs, D., & Fuchs, L. S. (2006). Introduction to response to intervention: What, why, and how valid is it? Reading Research Quarterly, 41, 93–99. doi:10.1598/RRQ.41.1.4
   Web of Science ®Google Scholar
• Georges, A., Brooks-Gunn, J., & Malone, L. M. (2012). Links between young children's behavior and achievement: The role of social class and classroom composition. American Behavioral Scientist, 56(7), 961–990. doi:10.1177/0002764211409196
   Web of Science ®Google Scholar
• Grimm, K. J., Ram, N., & Estabrook, R. (2010). Nonlinear structured growth mixture models in M plus and OpenMx. Multivariate Behavioral Research, 45(6), 887–909. doi:10.1080/00273171.2010.531230
   PubMed Web of Science ®Google Scholar
• Hinshaw, S. P. (1992). Externalizing behavior problems and academic underachievement in childhood and adolescence: Causal relationships and underlying mechanisms. Psychological Bulletin, 111(1), 127–155. doi:10.1037/0033-2909.111.1.127
   PubMed Web of Science ®Google Scholar
• Hipp, J. R., & Bauer, D. J. (2006). Local solutions in the estimation of growth mixture models. Psychological Methods, 11(1), 36–53. doi:10.1037/1082-989X.11.1.36
   PubMed Web of Science ®Google Scholar
• Horner, R. H., Swaminathan, H., Sugai, G., & Smolkowski, K. (2012). Considerations for the systematic analysis and use of single-case research. Education and Treatment of Children, 35(2), 269–290. doi:10.1353/etc.2012.0011
   Web of Science ®Google Scholar
• Johnson, A. H., Miller, F. G., Chafouleas, S. M., Welsh, M. E., Riley-Tillman, T. C., & Fabiano, G. A. (2016). Evaluating the technical adequacy of DBR-SIS in tri-annual behavioral screening: A multisite investigation. Journal of School Psychology, 54, 39–57.
   PubMed Web of Science ®Google Scholar
• Jung, T., & Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2(1), 302–317. doi:10.1111/j.1751-9004.2007.00054.x
   Google Scholar
• Kazdin, A. E. (1982). Single-case research designs: Methods for clinical and applied settings. Oxford, UK: Oxford University Press.
   Google Scholar
• Kamphaus, R. W., Huberty, C., DiStefano, C., & Petoskey, M. (1997). A typology of teacher-rated child behavior for a national U.S. sample. Journal of Abnormal Child Psychology, 25(6), 453–463. doi:10.1023/A:1022681630818
   PubMed Web of Science ®Google Scholar
• Kamphaus, R. W., & Reynolds, C. R. (2007). BASC-2 Behavioral and emotional screening system. Circle Pines, MN: Pearson.
   Google Scholar
• Kellam, S. G., Wang, W., Mackenzie, A. C., Brown, C. H., Ompad, D. C., Or, F., … Windham, A. (2014). The impact of the Good Behavior Game, a universal classroom-based preventive intervention in first and second grades, on high-risk sexual behaviors and drug abuse and dependence disorders into young adulthood. Prevention Science, 15(1), 6–18. doi:10.1007/s11121-012-0296-z
   Google Scholar
• Kim, S., Orpinas, P., Martin, R., Horne, A. M., Sullivan, T. N., & Hall, D. B. (2010). A typology of behavioral adjustment in ethnically diverse middle school students. Journal of Psychoeducational Assessment, 28(6), 524–535. doi:10.1177/0734282909352801
   Web of Science ®Google Scholar
• Kline, R. B. (2011). Principles and practice of structural equation modeling (3rd ed.). New York: Guilford Press.
   Google Scholar
• Kooken, J. (2014). Model Selection for Data that Lack Normality. (Unpublished doctoral comprehensive paper). University of Connecticut, Storrs, CT.
   Google Scholar
• Kratochwill, T. R., Hitchcock, J. H., Horner, R. H., Levin, J. R., Odom, S. L., Rindskopf, D. M., … Shadish, W. R. (2013). Single-case intervention research design standards. Remedial and Special Education, 34(1), 26–38. doi:10.1177/0741932512452794
   Web of Science ®Google Scholar
• Kuntsche, E., Otten, R., & Labhart, F. (2015). Identifying risky drinking patterns over the course of Saturday evenings: An event-level study. Psychology of Addictive Behavior, 29(3), 744–752. doi:10.1037/adb0000057
   PubMed Web of Science ®Google Scholar
• Liu, M., & Hancock, G. (2014). Unrestricted mixture models for class identification in growth mixture modeling. Educational and Psychological Measurement, 74(4), 557–584. doi:10.1177/0013164413519798
   Web of Science ®Google Scholar
• Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88(3), 767–778. doi:10.1093/biomet/88.3.767
   Web of Science ®Google Scholar
• Marsh, H. W., & Hau, K.-T. (2007). Applications of latent-variable models in educational psychology: The need for methodological-substantive synergies. Contemporary Educational Psychology, 32, 151–170. doi:10.1016/j.cedpsych.2006.10.008
   Web of Science ®Google Scholar
• McClelland, M. M., Acock, A. C., & Morrison, F. J. (2006). The impact of kindergarten learning-related skills on academic trajectories at the end of elementary school. Early Childhood Research Quarterly, 21(4), 471–490. doi:10.1016/j.ecresq.2006.09.003
   Web of Science ®Google Scholar
• McCoach, D. (2010). Hierarchical linear modeling. In Hancock, G. (Eds.), The reviewer's guide to quantitative methods in the social sciences (pp. 123–140). New York: Routledge.
   Google Scholar
• McCoach, D. Betsy, and Anne C. Black. (2008). Evaluation of model fit and adequacy, Multilevel modeling of educational data: 245–272.
   Google Scholar
• Morin, A. J. S., Maïano, C., Nagengast, B., Marsh, H. W., Morizot, J., & Janosz, M. (2011). General growth mixture analysis of adolescents' developmental trajectories of anxiety: The impact of untested invariance assumptions on substantive interpretations. Structural Equation Modeling: A Multidisciplinary Journal, 18(4), 613–648. doi:10.1080/10705511.2011.607714
   Web of Science ®Google Scholar
• Morin, A. J. S., Maïano, C., Marsh, H. W., Nagengast, B., & Janosz, M. (2013). School life and adolescents' self-esteem trajectories. Child Development, 84(6), 1967–1988. doi:10.1111/cdev.12089
   PubMed Web of Science ®Google Scholar
• Muthén, B. O. (2001). Second generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In A. Sayer & L. Collins (Eds.), New methods for the analysis of change (pp. 291–322). Washington, DC: American Psychological Association.
   Google Scholar
• Muthén, B. O. (2004). Latent variable analysis. In D. Kaplan (Ed.), The Sage handbook of quantitative methodology for the social sciences, (pp. 345–368). Thousand Oaks, CA: Sage.
   Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2014). Mplus User's Guide. Seventh Edition. Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM Algorithm. Biometrics, 55(2), 463–469. doi:10.1111/j.0006-341X.1999.00463.x
   PubMed Web of Science ®Google Scholar
• Nagin, D. S. (1999). Analyzing developmental trajectories: A semiparametric, group-based approach. Psychological Methods, 4(2), 139–157. doi:10.1037/1082-989X.4.2.139
   Web of Science ®Google Scholar
• No Child Left Behind (NCLB). (2003). Act of 2001, 20 U.S.C.A. § 6301 et seq. (West 2003).
   Google Scholar
• Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 14(4), 535–569. doi:10.1080/10705510701575396
   Web of Science ®Google Scholar
• Owen, J., Adelson, J., Budge, S., Wampold, B., Kopta, M., Minami, T., … Miller, S. (2015). Trajectories of change in psychotherapy. Journal of Clinical Psychology, 71(9), 817–827. doi:10.1002/jclp.22191
   PubMed Web of Science ®Google Scholar
• Palardy, G. J., & Vermunt, J. K. (2010). Multilevel growth mixture models for classifying groups. Journal of Educational and Behavioral Statistics, 35(5), 532–565. doi:10.3102/1076998610376895
   Web of Science ®Google Scholar
• Petras, H., & Masyn, K. (2010). General growth mixture analysis with antecedents and consequences of change. In A. A. Piquero & D. Weisburd (Eds.), Handbook of quantitative criminology (pp. 69–100). New York, NY: Springer.
   Google Scholar
• Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology, 48(1), 85–112. doi:10.1016/j.jsp.2009.09.002
   PubMed Web of Science ®Google Scholar
• Ram, N., & Grimm, K. J. (2009). Methods and measures: Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33(6), 565–576. doi:10.1177/0165025409343765
   PubMed Web of Science ®Google Scholar
• Ramaswamy, V., DeSarbo, W. S., Reibstein, D. J., & Robininson, W. T. (1993). An empirical pooling approach for estimating marketing mix elasticities with PIMS data. Marketing Science, 12, 103–124. doi:10.1287/mksc.12.1.103
   Web of Science ®Google Scholar
• Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage.
   Google Scholar
• Riley-Tillman, T. C., & Burns, M. K. (2009). Evaluating educational interventions: Single-case design for measuring response to intervention. New York, NY, USA: Guilford Press
   Google Scholar
• Simmons, D. C., Kim, M., Kwok, O. M., Coyne, M. D., Simmons, L. E., Oslund, E., … Rawlinson, D. A. (2015). Examining the effects of linking student performance and progression in a Tier 2 kindergarten reading intervention. Journal of Learning Disabilities, 48(3), 255–270. doi:10.1177/0022219413497097
   PubMed Web of Science ®Google Scholar
• Tofighi, D., & Enders, C. K. (2008). Identifying the correct number of classes in growth mixture models. In G. R. Hancock & K. M. Samuelson (Eds.), Advances in latent variable mixture models (pp. 317–341). Charlotte, NC: Information Age.
   Google Scholar
• Wentzel, K. R. (1993). Does being good make the grade? Social behavior and academic competence in middle school. Journal of Educational Psychology, 85(2), 357–364. doi:10.1037/0022-0663.85.2.357
   Web of Science ®Google Scholar
• White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica: Journal of the Econometric Society, 1–25.
   Web of Science ®Google Scholar