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.
|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.
Data and analysis code (R and SAS): Download zip file
- 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).
- 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).
- 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).
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
- Kalénine, S., Mirman, D., and Buxbaum, L. J. (in press). A
combination of thematic and similarity-based semantic processes confers
resistance to deficit following left hemisphere stroke. Frontiers in Human Neuroscience.
- Kalénine, S., Mirman, D., Middleton, E. L., and Buxbaum, L. J. (in press). Temporal dynamics of activation of thematic and functional knowledge during conceptual processing of manipulable artifacts. Journal of Experimental Psychology: Learning, Memory, and Cognition. DOI: 10.1037/a0027626.
- Lee, C.-L., Middleton, E. L., Mirman, D., Kalénine, S., and Buxbaum, L. J. (in press). Incidental and context-responsive activation of structure- and function-based action features during object identification. Journal of Experimental Psychology: Human Perception and Performance. DOI: 10.1037/a0027533.
- Mirman, D. and Graziano, K.M. (in press). Individual differences in strength of taxonomic versus thematic relations. Journal of Experimental Psychology: General. DOI: 10.1037/a0026451
- Revill, K.P. and Spieler, D.H. (2012). The effect of lexical frequency on spoken word recognition in young and older listeners. Psychology and Aging, 27(1), 80-87. doi: 10.1037/a0024113.
- Brown, M., Salverda, A.P., Dilley, L.C., and Tanenhaus, M.K. (2011). Expectations from preceding prosody influence segmentation in online sentence processing. Psychonomic Bulletin & Review, 18(6), 1189-1196. DOI: 10.3758/s13423-011-0167-9.
- Magnuson, J.S., Kukona, A., Braze, D., Johns, C.L., Van Dyke, J.A., Tabor, W., Mencl, W.E., Pugh, K.R., and Shankweiler, D.P. (2011). Phonological Instability in Young Adult Poor Readers. In McCardle, P., Miller, B., Lee, J.R., Tzeng, O.J.L. (Eds.), Dyslexia Across Languages, Orthography and the Brain-Gene-Behavior Link. Paul H. Brookes Publishing Co. (pp. 184-201).
- Kukona, A., and Tabor, W. (2011). Impulse Processing: A dynamical systems model of incremental eye movements in the Visual World Paradigm. Cognitive Science, 35(6), 1009-1051. DOI: 10.1111/j.1551-6709.2011.01180.x.
- Mirman, D., Yee, E., Blumstein, S., and Magnuson, J.S. (2011). Theories of spoken word recognition deficits in aphasia: Evidence from eye-tracking and computational modeling. Brain & Language, 117, 53-68.
- Kukona, A., Fang, S-Y., Aicher, K.A., Chen, H., and Magnuson, J.S. (2011). The time course of anticipatory constraint integration. Cognition, 119(1), 23-42.
J.C. and Papafragou, A. (2010).
Perceiving and remembering
events cross-linguistically: Evidence from dual-task paradigms.
Journal of Memory and Language, 63(1), 64-82.
- Malins, J.G. and Joanisse, M.F. (2010). The roles of tonal and segmental information in Mandarin spoken word recognition: An eyetracking study. Journal of Memory and Language, 62(4), 407-420.
- Mirman, D., Strauss, T.J., Dixon, J.A., and Magnuson, J.S. (2010). Effect of representational distance between meanings on recognition of ambiguous spoken words. Cognitive Science, 34(1), 161-173.
- Pirog Revill, K. and Spieler, D.H. (2009). The Time Course of Lexical Competition in Young and Older Adults. In N. A. Taatgen & H. van Rijn (Eds.) Proceedings of the 31st Annual Cognitive Science Society Meeting (pp. 261-266). Austin, TX: Cognitive Science Society.
- Mirman, D. and Magnuson, J.S. (2009b). Dynamics of activation of semantically similar concepts during spoken word recognition. Memory & Cognition, 37(7), 1026-1039.
- Magnuson, J. S., Dixon, J., Tanenhaus, M. K., & Aslin, R. N. (2007). The dynamics of lexical competition during spoken word recognition. Cognitive Science, 31, 133-156.
- 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:
- 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