Growth Curve Analysis of VWP Data


Growth curve analysis (GCA) is a multilevel orthogonal polynomial curve-fitting approach designed for analysis of time-course data. This method can be applied to visual world paradigm (VWP) data to analyze effects of experimental manipulations (e.g., word frequency) and to analyze individual differences.

Original article

Mirman, D. Dixon, J.A., & Magnuson, J.S. (2008). Statistical and computational models of the visual world paradigm: Growth curves and individual differences. Journal of Memory and Language, 59(4), 475-494.

Abstract: Time course estimates from eye tracking during spoken language processing (the "visual world paradigm", or VWP) have enabled progress on debates regarding fine-grained details of activation and competition over time. There are, however, three gaps in current analyses of VWP data: consideration of time in a statistically rigorous manner, quantification of individual differences, and distinguishing linguistic effects from non-linguistic effects. To address these gaps, we have developed an approach combining statistical and computational modeling. The statistical approach (growth curve analysis, a technique explicitly designed to assess change over time at group and individual levels) provides a rigorous means of analyzing time course data. We introduce the method and its application to VWP data. We also demonstrate the potential for assessing whether differences in group or individual data are best explained by linguistic processing or decisional aspects of VWP tasks through comparison of growth curve analyses and computational modeling, and discuss the potential benefits for studying typical and atypical language processing.
  1. Simple case testing difference between two within-subject conditions. Analysis of effects of word frequency, neighborhood density, and cohort density on target fixations. This example corresponds to "Analysis of Target Fixations". The data are from Magnuson et al. (2007).
  2. This example tests for differences between fixations of cohort, rhyme, and unrelated competitors. This example corresponds to "Analysis of Competitor Fixations". The data are from Magnuson et al. (2003).
  3. This example tests for individual differences in frequency and cohort density effects. This example corresponds to "Individual Differences in VWP Data". The data are from Magnuson et al. (2007).
Data and analysis code (R and SAS): Download zip file


Here are materials from my workshops on using multilevel models (growth curve analysis) to analyze eye tracking data. (Both workshops were in Feb. 2010, one at MRRI and one sponsored by the Cognitive Science Program at Northwestern University).

A good place to start is Part 1: Conceptual Foundations. This presentation lays out the motivation and basic principles of growth curve analysis.

Part 2 is a step-by-step walk through an example of a growth curve analysis of data from a typical "visual world" eye tracking experiment (Mirman & Magnuson, 2009b). The presentation describes the experiment, analysis procedure, and results. The zipped archive contains the data file (SemanticCompetitionExample.txt) and the analysis script (gca_script.r) to go with that example.

How to use residual (aka "random") effects to quantify individual differences is described in Part 3: Individual Differences. That presentation gives one example (Mirman, Yee, Blumstein, & Magnuson, 2011) and the zip archive contains a script (gca_indivDiffs.r) for running a similar individual differences analysis on the walkthrough example data.

Related Technical Reports

LCDL TR2011.01: Choosing between lme and lmer for Growth Curve Analysis

Papers using this method

*** This list has not been updated since 2012. If you are very interested in papers that directly reference this method, try Google Scholar ***

Eye tracking / VWP

Other applications

  • Zwaan, R.A., van der Stoep, N., Guadalupe, T., & Bouwmeester, S. (2012) Language Comprehension in the Balance: The Robustness of the Action-Compatibility Effect (ACE). PLoS ONE 7(2): e31204. doi:10.1371/journal.pone.0031204.
  • Stephen, D. G., & Hajnal, A. (2011). Transfer of calibration between hand and foot: Functional equivalence and fractal fluctuations. Attention, Perception & Psychophysics, 73(5), 1302-1328. doi: 10.3758/s13414-011-0142-6
  • Stephen, D.G. & Anastas, J. (2011). Fractal fluctuations in gaze speed visual search. Attention, Perception, & Psychophysics, 73(3), 666-677.
  • Boncoddo, R., Dixon, J.A., Kelley, E. (2010). The emergence of a novel representation from action: Evidence from preschoolers. Developmental Science, 13(2), 370-377.
  • Stephen, D. G., Arzamarski, R., and Michaels, C. F. (2010). The role of fractality in perceptual learning: Exploration in dynamic touch. Journal of Experimental Psychology: Human Perception & Performance, 36(5), 1161-1173.
  • Boncoddo, R. A., Dixon, J. A., and Kelley, E. (2010). The emergence of a novel representation from action: evidence from preschoolers. Developmental Science, 13(2), 370-377.
  • Stephen, D. G., Boncoddo, R. A., Magnuson, J. S., and Dixon, J. A. (2009). The dynamics of insight: Mathematical discovery as a phase transition. Memory & Cognition, 37, 1132-1149.
  • Mirman, D., Magnuson, J.S., Graf Estes, K., and Dixon, J.A. (2008). The link between statistical segmentation and word learning in adults. Cognition, 108(1), 271-280.

Other online resources

Dan Mirman,
Sep 26, 2016, 2:42 PM
Dan Mirman,
Feb 10, 2011, 7:47 AM
Dan Mirman,
Feb 28, 2010, 12:21 PM
Dan Mirman,
Feb 28, 2010, 12:27 PM
Dan Mirman,
Feb 28, 2010, 12:27 PM
Dan Mirman,
Feb 28, 2010, 12:27 PM