Latent Growth Models with Floors, Ceilings, and Random Knots

References

• Arshad, M. (2006). Network analysis and synthesis. New Delhi: Laxmi Publications.
   Google Scholar
• Asparouhov, T., & Muthén, B. (2010). Simple second order chi-square correction (unpublished manuscript). Retrieved from https://www.statmodel.com/download/WLSMV_new_chi21.pdf.
   Google Scholar
• Bates, D. M., & Watts, D. G. (1988). Nonlinear regression analysis and its applications. New York: Wiley.
   Google Scholar
• Blozis, S. A. (2004). Structured latent curve models for the study of change in multivariate repeated measures. Psychological Methods, 9(3), 334–353. doi:10.1037/1082-989X.9.3.334
   PubMed Web of Science ®Google Scholar
• Blozis, S. A. (2007a). A second-order structured latent curve model for longitudinal data. In K. van Montfort, H. Oud, & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences (pp. 189–214). Mahwah, NJ: Erlbaum.
   Google Scholar
• Blozis, S. A. (2007b). On fitting nonlinear latent curve models to multiple variables measured longitudinally. Structural Equation Modeling: A Multidisciplinary Journal, 14(2), 179–201. doi:10.1080/10705510709336743
   Web of Science ®Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.
   Google Scholar
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. New York: Wiley.
   Google Scholar
• Browne, M. W. (1993). Structured latent curve models. In C. M. Cuadras & C. R. Rao (Eds.), Multivariate analysis: Future directions 2 (pp. 171–197). Amsterdam: Elsevier-North Holland.
   Google Scholar
• Browne, M. W., & Du Toit, S. H. C. (1991). Models for learning data. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change. Washington, DC: American Psychological Association.
   Google Scholar
• Choi, J., Harring, J. R., & Hancock, G. R. (2009). Latent growth modeling for logistic response functions. Multivariate Behavioral Research, 44(5), 620–645. doi:10.1080/00273170903187657
   Web of Science ®Google Scholar
• Chou, C.-P., Yang, D., Pentz, M. A., & Hser, Y.-I. (2004). Piecewise growth curve modeling approach for longitudinal prevention study. Computational Statistics & Data Analysis, 46, 213–225. doi:10.1016/S0167-9473(03)00149-X
   Web of Science ®Google Scholar
• Connor, C. M., Morrison, F. J., & Slominski, L. (2006). Preschool instruction and children's emergent literacy growth. Journal of Educational Psychology, 98(4), 665–689. doi:10.1037/0022-0663.98.4.665
   Web of Science ®Google Scholar
• Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7(1), 41–63. doi:10.1037/1082-989X.7.1.41
   PubMed Web of Science ®Google Scholar
• Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38(4), 529–569. doi:10.1207/s15327906mbr3804_5
   PubMed Web of Science ®Google Scholar
• DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling: A Multidisciplinary Journal, 21(3), 425–438. doi:10.1080/10705511.2014.915373
   Web of Science ®Google Scholar
• Duncan, T. E., Duncan, S. C., & Strycker, L. A. (2006). An introduction to latent variable growth curve modeling: Concepts, issues, and applications (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.
   Google Scholar
• Finney, S., & Distefano, C. (2013). Nonnormal and categorical data in structural equation modeling. In G. R. Hancock, & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 439–492). Charlotte, NC: Information Age Publishing, Inc.
   Google Scholar
• Fitzmaurice, G., Laird, N., & Ware, J. (2011). Applied longitudinal analysis (2nd ed.). Hoboken, NJ: Wiley.
   Google Scholar
• Flora, D. B. (2008). Specifying piecewise latent trajectory models for longitudinal data. Structural Equation Modeling: A Multidisciplinary Journal, 15(3), 513–533. doi:10.1080/10705510802154349
   Web of Science ®Google Scholar
• Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 676–701. doi:10.1080/10705510903206055
   PubMed Web of Science ®Google Scholar
• Hancock, G. R., Harring, J. R., & Lawrence, F. R. (2013). Using latent growth models to evaluate longitudinal change. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 309–341). Charlotte, NC: Information Age Publishing, Inc.
   Google Scholar
• Hancock, G. R., Kuo, W.-L., & Lawrence, F. (2001). An illustration of second-order latent growth models. Structural Equation Modeling: A Multidisciplinary Journal, 8(3), 470–489. doi:10.1207/S15328007SEM0803_7
   Web of Science ®Google Scholar
• Harring, J. R., Cudeck, R., & Du Toit, S. H. C. (2006). Fitting partially nonlinear random coefficient models as SEMs. Multivariate Behavioral Research, 41(4), 579–596. doi:10.1207/s15327906mbr4104_7
   PubMed Web of Science ®Google Scholar
• Long, J. S. (1997). Regression models for categorical and limited dependent variables. Thousand Oaks, CA: Sage Publications.
   Google Scholar
• MacCallum, R. C., Kim, C., Malarkey, W. B., & Kiecolt-Glaser, J. K. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32(3), 215–253. doi:10.1207/s15327906mbr3203_1
   PubMed Web of Science ®Google Scholar
• Marsh, L. C., & Cormier, D. R. (2001). Spline regression models. Thousand Oaks, CA: Sage.
   Google Scholar
• McArdle, J. J., & Wang, L. (2008). Modeling age-based turning points in longitudinal life-span growth curves of cognition. In P. Cohen (Ed.), Applied data analytic techniques for turning points research (pp. 105–127). New York: Routledge.
   Google Scholar
• McNeish, D., & Matta, T. (2018). Differentiating between mixed-effects and latent-curve approaches to growth modeling. Behavior Research Methods, 50(4), 1398–1414. doi:10.3758/s13428-017-0976-5
   PubMed Web of Science ®Google Scholar
• Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55(1), 107–122. doi:10.1007/BF02294746
   Web of Science ®Google Scholar
• Muthén, B. O. (1989). Tobit factor analysis. British Journal of Mathematical and Statistical Psychology, 42(2), 241–250. doi:10.1111/j.2044-8317.1989.tb00913.x
   Google Scholar
• Muthén, B. O., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of nonnormal Likert variables. British Journal of Mathematical and Statistical Psychology, 38(2), 171–189. doi:10.1111/j.2044-8317.1985.tb00832.x
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (1998–2017). Mplus user’s guide (8th ed.). Los Angeles, CA: Muthén & Muthén.
   Google Scholar
• Preacher, K. J., & Hancock, G. R. (2012). On interpretable reparameterizations of linear and nonlinear latent growth curve models. In J. R. Harring & G. R. Hancock (Eds.), Advances in longitudinal methods in the social and behavioral sciences (pp. 25–58). Charlotte, NC: Information Age Publishing, Inc.
   Google Scholar
• Preacher, K. J., & Hancock, G. R. (2015). Meaningful aspects of change as novel random coefficients: A general method for reparameterizing longitudinal models. Psychological Methods, 20(1), 84–101. doi:10.1037/met0000028
   PubMed Web of Science ®Google Scholar
• Preacher, K. J., Wichman, A., MacCallum, R. C., & Briggs, N. E. (2008). Latent growth curve modeling. Thousand Oaks, CA: Sage Publications.
   Google Scholar
• RStudio Team. (2015). RStudio: Integrated development for R. Boston, MA: RStudio, Inc. Retrieved from http://www.rstudio.com/.
   Google Scholar
• Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507–514. doi:10.1007/BF02296192
   Web of Science ®Google Scholar
• Satorra, A., & Bentler, P. M. (2010). Ensuring positiveness of the scaled difference chi-square test statistic. Psychometrika, 75(2), 243–248. doi:10.1007/s11336-009-9135-y
   PubMed Web of Science ®Google Scholar
• Seber, G. A. F., & Wild, C. J. (1989). Nonlinear regression. New York: Wiley.
   Google Scholar
• Sterba, S. K. (2014). Fitting nonlinear latent growth curve models with individually varying time points. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 630–647. doi:10.1080/10705511.2014.919828
   Web of Science ®Google Scholar
• Stoel, R. D., Garre, F. G., Dolan, C., & Van Den Wittenboer, G. (2006). On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods, 11(4), 439–455. doi:10.1037/1082-989X.11.4.439
   PubMed Web of Science ®Google Scholar
• Twisk, J., & Rijmen, F. (2009). Longitudinal Tobit regression: A new approach to analyze outcome variables with floor or ceiling effects. Journal of Clinical Epidemiology, 62(9), 953–958. doi:10.1016/j.jclinepi.2008.10.003
   PubMed Web of Science ®Google Scholar
• Wang, L., Zhang, Z., McArdle, J. J., & Salthouse, T. A. (2008). Investigating ceiling effects in longitudinal data analysis. Multivariate Behavioral Research, 43(3), 476–496. doi:10.1080/00273170802285941
   Web of Science ®Google Scholar
• Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson III tests of achievement. Itasca, IL: Riverside Publishing.
   Google Scholar
• Xia, Y. (2016). Investigating the chi-square-based model-fit indexes for WLSMV and ULSMV estimators (Doctoral dissertation). Retrieved from http://purl.flvc.org/fsu/fd/FSU_2016SU_Xia_fsu_0071E_13379.
   Google Scholar