Abstract
In recent years, statistical methods for latent growth modeling have been commonly used in educational and psychological research. The purpose of this chapter is to illustrate growth modeling of change in pattern using multidimensional scaling (MDS) in the context of growth mixture modeling (GMM). We discuss how MDS growth pattern analysis may differ with respect to modeling changes in level, as commonly done with GMM, given that they have similarities in terms of model estimation, latent group identification, classification of individuals, and the interpretation of growth trajectory. We discuss the MDS growth pattern analysis in particular since it is less known. Using two simulated data sets as well as actual data from the Early Childhood Longitudinal Study of the Kindergarten Class of 1998–99 (ECLS-K) study, we demonstrate differences in growth pattern vs. level. It is our goal to provide researchers with a better idea of what MDS growth pattern analysis can accomplish, which may provide them with the knowledge to appropriately utilize this type of analysis in their own research.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
As indicated by Ram and Grimm (2009), latent growth modeling is a generic term that include various similar growth modeling approaches, such as latent trajectory analysis, latent curve modeling, mixed effects models of change, and multilevel models of change.
- 2.
In MDS, dimensions are defined as a set of m directed axes that are orthogonal to each other in a geometric space. In the applied context, dimensions may be viewed as underlying representations of how the points may form certain groupings, which would meaningfully explain the data. This concept is similar to latent classes or factors in mixture modeling. Distance is defined as distribution of points along k dimension among pairs of objects (e.g., time points) in a plane that shows changes.
- 3.
The issue of setting the origin for each dimension in the PAMS model corresponds to the “centering” issue in multiple regression. That is, just as the interpretation of the intercept parameter in multiple regression changes depending on how the predictor variables are centered, the interpretation of the intercept parameter in latent growth curve models changes depending on placement of the zero point along each growth dimension.
References
Aber, M. S., & McArdle, J. J. (1991). Latent growth curve approach to modeling the development of competence. In M. Chandler & M. Chapman (Eds.), Criteria for competence: Controversies in the conceptualization and assessment of children's abilities (pp. 231–258). Mahwah, NJ: Lawrence Erlbaum Associates.
Asparouhov, T., & Muthén, B. (2012). Auxiliary variables in mixture modeling: A 3-step approach using Mplus. statmodel.com.
Boscardin, C., Muthén, B., Francis, D., & Baker, E. (2008). Early identification of reading difficulties using heterogeneous developmental trajectories. Journal of Educational Psychology, 100, 192–208.
Collins, L. M., & Horn, J. L. (1991). Best methods for the analysis of change: Recent advance, unanswered questions, future directions. Washington, DC: American Psychological Association.
Cudeck, R., & Henly, S. J. (2003). A realistic perspective on pattern representation in growth data: Comment on Bauer and Curran (2003). Psychological Methods, 8(3), 378–383.
Davison, M. L., Davenport, E., Bielinski, J., Ding, S., Kuang, H., Li, F., et al. (1995). Utilizing profile analysis via multidimensional scaling to ascertain patterns in course-taking: Mathematics and science course-taking patterns. Paper presented at the AERA, San Francisco, CA.
Davison, M. L., Gasser, M., & Ding, S. (1996). Identifying major profile patterns in a population: An exploratory study of WAIS and GATB patterns. Psychological Assessment, 8, 26–31.
Davison, M. L., Kuang, H., & Kim, S. (1999). The structure of ability profile patterns: A multidimensional scaling perspective on the structure of intellect. In P. L. Ackerman, P. C. Kyllonen, & R. D. Roberts (Eds.), Learning and individual differences: Process, trait, and content determinants (pp. 187–204). Washington, DC: APA Books.
Denton, K., West, J., & Walston, J. (2003). Reading—Young children’s achievement and classroom experiences, NCES 2003–070. Washington, DC: U.S. Department of Education, National Center for Education Statistics.
Ding, C. S. (2005). Applications of multidimensional scaling profile analysis in developmental research: An example using adolescent irritability patterns. International Journal of Behavioral Development, 29(3), 185–196.
Ding, C. S. (2007a). Modeling growth data using multidimensional scaling profile analysis. Quality & Quantity, 41(6), 891–903.
Ding, C. S. (2007b). Studying growth heterogeneity with multidimensional scaling profile analysis. International Journal of Behavioral Development, 31(4), 347–356.
Ding, C. S., & Davison, M. L. (2005). A longitudinal study of math achievement gains for initially low achieving students. Contemporary Educational Psychology, 30, 81–95.
Ding, C. S., Davison, M. L., & Petersen, A. C. (2005). Multidimensional scaling analysis of growth and change. Journal of Educational Measurement, 42, 171–191.
Ding, C. S., & Navarro, V. (2004). An examination of student mathematics learning as assessed by SAT 9: A longitudinal look. Studies in Education Evaluation, 30, 237–253.
Friedman, L. (1989). Mathematics and the gender gap: A meta-analysis of recent studies on sex differences in mathematical tasks. Review of Educational Research, 59, 185–213.
Hallquist, M. N., & Lenzenweger, M. F. (2012). Identifying latent trajectories of personality disorder symptom change: Growth mixture modeling in the longitudinal study of personality disorders. Journal of Abnormal Psychology. doi:10.1037/a0030060.
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.
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.
Muthen, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557–587.
Muthen, B. (2001). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling. In L. M. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 291–322). Washington, DC: American Psychological Association.
Muthen, L. K., & Muthen, B. O. (1998–2007). Mplus user's guide (5th ed.). Los Angeles, CA: Muthén & Muthén.
Muthén, L. K., & Muthén, B. O. (2001). Mplus: Statistical analysis with latent variables. Los Angeles, CA: Muthén & Muthén.
Nagin, D. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4, 139–177.
Princiotta, D., Flanagan, K. D., & Germino Hausken, E. (2006). Fifth grade: Findings from the fifth grade follow-up of the early childhood longitudinal study, kindergarten class of 1998–99 (ECLS-K). Washington, DC: National Center for Education Statistics.
Ram, N., & Grimm, K. (2009). Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33(6), 565–576.
SAS Institute Inc. (2011). SAS/STAT ® 9.3 User’s guide. Cary, NC: SAS Institute Inc.
Vermunt, J. K. (2010). Latent class modeling with covariates: Two improved three-step approaches. Political Analysis, 18, 450–469.
Wang, M., & Bodner, T. E. (2007). Growth mixture modeling: Identifying and predicting unobserved subpopulations with longitudinal data. Organizational Research Methods, 10(4), 635–656. doi:10.1177/1094428106289397.
Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363–381.
Williamson, G. L., Appelbaum, M., & Epanchin, A. (1991). Longitudinal analyses of academic achievement. Journal of Educational Measurement, 28, 61–76.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ding, C. (2015). Studying Behavioral Change: Growth Analysis via Multidimensional Scaling Model. In: Stemmler, M., von Eye, A., Wiedermann, W. (eds) Dependent Data in Social Sciences Research. Springer Proceedings in Mathematics & Statistics, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-319-20585-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-20585-4_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20584-7
Online ISBN: 978-3-319-20585-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)