Visual-Graphical Methods for Exploring Longitudinal Data

Longitudinal data typically have the characteristics of changes over time, nonlinear growth patterns, between-subjects variability, and the within errors exhibiting heteroscedasticity and dependence. The data exploration is more complicated than that of cross-sectional data. The purpose of this paper is to organize/integrate of various visual-graphical techniques to explore longitudinal data. From the application of the proposed methods, investigators can answer the research questions include characterizing or describing the growth patterns at both group and individual level, identifying the time points where important changes occur and unusual subjects, selecting suitable statistical models, and suggesting possible within-error variance.

Authors:

• H. W. Ker

Keywords:

• Data exploration
• exploratory analysis
• HLMs/LMEs
• longitudinal data
• visual-graphical methods.

References:

[1] Bates, D. M., & Pinheiro, J. C. (1997). Software design for longitudinal
data analysis. In T. G. Gregoire, D. R. Brillinger, P. J. Diggle, E.
Russek-Cohen, W. G. Warren, & R. D. Wolfinger (Ed.), Modeling
longitudinal and spatially correlated data: methods, application and
further direction (pp. 37-48). New York: Springer-Verlag.
[2] Behrens, J. T. (1997). Principles and procedures of exploratory data
analysis. Psychological Methods, 2, 131-160.
[3] Cleveland, W. S. (1993). Visualizing data. Summit, NJ: Hobart Press.
[4] Cudek, R. & Klebe, K. J. (2002). Multiphase mixed-effects models for
repeated measures data. Psychological Methods, 7, 41-63.
[5] Draper, D. (1995). Inference and hierarchical modeling in the social
science. Journal of Educaational and Behavioral Statistics, 20, 115-147.
[6] Hox, J. J. (2000). Multilevel analysis of grouped and longitudinal data. In
T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal
and multilevel data: Practical issues, applied approaches and specific
examples (pp. 15-32). NJ: Lawrence Erlbaum Associates.
[7] Peterson, M. S., & Kramer, A. F. (2001). Contextual cueing reduces
interferencee from task-irrelevant onset distractor. Visual Cognition, 8,
843-859.
[8] Pinherio, J. C., & Bates, D. M. (2000). Mixed-effects models in S and
S-Plus. New York: Springer-Verlag.
[9] Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis:
Modeling change and event occurrence. NEW YORK: Oxford University
Press.
[10] Stoolmiller, M. (2002). Visual-graphical techniques for the analysis of
growth curves: the shapes and predictors of growth in substance use for
the male adolescents. Retrieved October 12, 2002, from
http://www.oslc.org/users/mikes/sra2.html.
[11] Venables, W. N., & Ripley, B. D. (1999). Modern applied statistics with
S-Plus (3rd ed.). New York: Springer-Verlag.
[12] Wang, J. (1999). Reasons for hierarchical linear modeling: A reminder.
The Journal of Experimental Education, 68, 89-93.
[13] Verbeke, G. & Molenberghs, G. (2000). Linear mixed models for
longitudinal data. New York: Spring-Verlag.