Dynamical systems analysis applied to working memory data

Frontiers in Psychology

Volumn 5, Issue JUL, 2014, Pages

  Gasimova, Fidan ^a   Robitzsch, Alexander ^b   Wilhelm, Oliver ^a   Boker, Steven M ^c   Hu, Yueqin ^d   Hülür, Gizem ^e  

^a UNIVERSITY OF ULM   (Germany)

^b Innovation and Development of the Austrian School System   (Austria)

^c UNIVERSITY OF VIRGINIA   (United States)

^d TEXAS STATE UNIVERSITY   (United States)

^e HUMBOLDT UNIVERSITY   (Germany)

Author keywords

B spline imputation; Dynamical systems analysis; Intensive longitudinal data; Intraindividual variability; Simulation study

Indexed keywords

EID: 84904886641     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2014.00687     Document Type: Article

References (53)

1. Bates, M. D. (2011). Package 'splines'. R Version 2.13.0. Priority base. Imports graphics, stats. Title Regression Spline Functions and Classes. Available online at: http://cran.r-project.org/web/packages/splines/
2. Bates, M. D., Maechler, M., and Bolker, B. (2011). Package 'lme4'. Version 0.999375-41: linear mixed-effects models using S4 classes. Available online at: http://cran.r-project.org/web/packages/lme4/lme4.pdf
3. Bergstrom, A. R. (1988). The history of continuous-time econometric models. Econ. Theory 4, 365-383. doi: 10.1017/S0266466600013359
4. Bermúdez, J. L. (2010). "New horizons: dynamical systems and situated cognition," in Cognitive Science: an Introduction to the Science of the Mind, ed J. L. Bermúdez (New York, NY: Cambridge University Press), 413-457.
5. Bisconti, T. L., Bergeman, C. S., and Boker, S. M. (2004). Emotional well-being in recently bereaved widows: a dynamical systems approach. J. Gerontol. Psychol. Sci. 59, 158-167. doi: 10.1093/geronb/59.4.P158
6. Bisconti, T. L., Bergeman, C. S., and Boker, S. M. (2006). Social support as a predictor of variability: an examination of the adjustment trajectories of recent widows. Psychol. Aging 21, 590-599. doi: 10.1037/0882-7974.21.3.590
7. Boker, S. M. (2001). "Differential structural equation modeling of intraindividual variability," in New Methods for the Analysis of Change, eds L. Collins and A. Sayer (Washington, DC: American Psychological Association), 5-25.
8. Boker, S. M. (2007). "Specifying latent differential equations models," in Data analytic Techniques for Dynamical Systems, eds S. M. Boker and M. J. Wenger (Mahwah, NJ: Erlbaum), 131-157.
9. Boker, S. M., and Bisconti, T. L. (2006). "Dynamical systems modeling of data from aging research," in Quantitative Methodology in Aging Research, eds C. S. Bergeman and S. M. Boker (Hillsdale, NJ: Lawrence Erlbaum Associates), 185-229.
10. Boker, S. M., Deboeck, P. R., Edler, C., and Keel, P. K. (2009). "Generalized local linear approximation of derivatives from time series," in Statistical Methods for Modeling Human Dynamics: an Interdisciplinary Dialogue, eds S.-M. Chow and E. Ferrar (Boca Raton, FL: Taylor and Francis), 161-178.
11. Boker, S. M., and Ghisletta, P. (2001). Random coefficients models for control parameters in dynamical systems. Multilevel Model. Newsl. 13, 10-17. Available online at: http://www.bristol.ac.uk/cmm/learning/support/new13-1.pdf
12. Boker, S. M., Montpetit, M. A., Hunter, M. D., and Bergeman, C. S. (2010a). "Modeling resilience with differential equations," in Learning and Development: Individual Pathways of Change, eds K. Newell and P. Molenaar (Washington, DC: American Psychological Association), 183-206.
13. Boker, S. M., Neale, M. C., and Rausch, J. R. (2004). "Latent differential equation modeling with multivariate multi-occasion indicators," in Recent Developments on Structural Equation Models: Theory and Applications, eds K. V. Montfort, J. Oud, and A. Satorra (Amsterdam, Kluwer: Kluwer Academic Publishers), 151-174.
14. Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., et al. (2010b). OpenMx version 1.0: Multipurpose Software for Statistical Modeling. Charlottesville, VA. Available online at: http://openmx.psyc.virginia.edu
15. Boker, S. M., and Nesselroade, J. R. (2002). A method for modeling the intrinsic dynamics of intraindividual variability: recovering the parameters of simulated oscillators in multi-wave panel data. Multivar. Behav. Res. 37, 127-160. doi: 10.1207/S15327906MBR3701_06
16. Bollen, K. A. (1989). Structural Equations with Latent Variables. New York, NY: Wiley-Interscience Publishers.
17. Brooks, S. P., and Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. J. Comput. Graph. Stat. 7, 434-455. doi: 10.2307/1390675
18. Brose, A., Schmiedek, F., Lövdén, M., and Lindenberger, U. (2012). Daily variability in working memory is coupled with negative affect: the role of attention and motivation. Emotion 12, 605-617. doi: 10.1037/a0024436
19. Cameron, A. C., and Trivedi, P. K. (2005). Microeconometrics: Methods and Applications. New York, NY: Cambridge University Press, 357-383.
20. Deboeck, P. R. (2010). Estimating dynamical systems, derivative estimation hints from SirRonald A. Fisher. Multivar. Behav. Res. 43, 725-745. doi: 10.1080/00273171.2010.498294
21. Deboeck, P. R., Montpetit, M., Bergeman, C., and Boker, S. M. (2009). Using derivative estimates to describe intraindividual variability at multiple time scales. Psychol. Methods 14, 367-386. doi: 10.1037/a0016622
22. Hu, Y., Boker, S., Neale, M., and Klump, K. L. (2014). Coupled latent differential equation with moderators: simulation and application. Psychol. Methods 19, 56-71. doi: 10.1037/a0032476
23. Hultsch, D. F., MacDonald, S. W. S., Hunter, M. A., Levy-Bencheton, J., and Strauss, E. (2000). Intraindividual variability in cognitive performance in older adults: comparison of adults with mild dementia, adults with arthritis, and healthy adults. Neuropsychology 14, 588-598. doi: 10.1037/0894-4105.14.4.588
24. Hülür, G., Wilhelm, O., and Robitzsch, A. (2011a). Multivariate Veränderungsmodelle für Schulnoten und Schülerleistungen in Deutsch und Mathematik [Multivariate change models for student achievement and school grades in German and mathematics]. Z. Entwicklungspsychol. Pädagog. Psychol. 43, 173-185. doi: 10.1026/0049-8637/a000051
25. Hülür, G., Wilhelm, O., and Schipolowski, S. (2011b). Prediction of self-reported knowledge with over-claiming, fluid and crystallized intelligence and typical intellectual engagement. Learn. Individ. Differ. 21, 742-746. doi: 10.1016/j.lindif.2011.09.006
26. Laird, N. M., and Ware, J. H. (1982). Random effects model for longitudinal data. Biometrics 38, 963-974.
27. Lumley, T. (2012). Package 'Mitools'. R Version 2.13.0. Tools for Multiple Imputation of Missing Data. Available online at: http://cran.r-project.org/web/packages/mitools/mitools.pdf
28. Little, R. J. A., and Rubin, D. B. (2002). Statistical Analysis with Missing Data. New York, NY: John Wiley.
29. Lunn, D. J., Thomas, A., Best, N. G., and Spiegelhalter, D. J. (2000). WinBUGS- a Bayesian modeling framework: concepts, structure and extensibility. Stat. Comput. 10, 321-333. doi: 10.1023/A:1008929526011
30. Nesselroade, J. R. (1990a). "Individual differences in intraindividual change," in Best Methods for the Analysis of Change: Recent Advances, Unanswered Questions, Future Directions, eds L. M. Collins and J. L. Horn (Washington, DC: American Psychological Association), 92-105.
31. Nesselroade, J. R., and Salthouse, T. A. (2004). Methodological and theoretical implications of intraindividual variability in perceptual-motor performance. J. Gerontol. B Psychol. Sci. Soc. Sci. 59, P49-P55. doi: 10.1093/geronb/59.2.P49
32. Nowak, A., and Lewenstein, M. (1994). "Dynamical systems: a tool for social psychology," in Dynamical Systems in Social Psychology, eds A. Nowak, R. Vallacher, and M. Lewenstein (San Diego, CA: Academic Press), 17-53.
33. Oberauer, K., Süß, H.-M., Schulze, R., Wilhelm, O., and Wittmann, W. W. (2000). Working memory capacity-facets of a cognitive ability construct. Pers. Individ. Differ. 29, 1017-1045. doi: 10.1016/S0191-8869(99)00251-2
34. Oberauer, K., Süß, H.-M., Wilhelm, O., and Wittmann, W. W. (2003). The multiple faces of working memory: storage, processing, supervision, and coordination. Intelligence 31, 167-193. doi: 10.1016/S0160-2896(02)00115-0
35. Oravecz, Z., Tuerlinckx, F., and Vandekerckhove, J. (2009). A hierarchical ornstein-uhlenbeck model for continuous repeated measurement data. Psychometrika 74, 395-418. doi: 10.1007/s11336-008-9106-8
36. Oud, J. H. L., and Folmer, H. (2011). Reply to steele and ferrer: modeling oscillation, approximately or exactly? Multivar. Behav. Res. 46, 985-993. doi: 10.1080/00273171.2011.625306
37. Ram, N., and Gerstorf, D. (2009). Time-structured and net intraindividual variability: tools for examining the development of dynamic characteristics and processes. Psychol. Aging 24, 778-791. doi: 10.1037/a0017915
38. Ram, N., Rabbitt, P., Stollery, B., and Nesselroade, J. R. (2005). Cognitive performance inconsistency: intraindividual change and variability. Psychol. Aging 20:623. doi: 10.1037/0882-7974.20.4.623
39. Racine, J. S. (2011). A Primer on Spline Regression. Available online at: http://www.stat.tamu.edu/~sinha/research/note1.pdf
40. Raudenbush, S. W., and Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Method, 2nd Edn. Newbury Park, CA: Sage.
41. R Development Core Team. (2012). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna. Available online at: http://www.R-project.org/. ISBN 3-900051-07-0
42. Rubin, D. B. (1987). Multiple Imputation for Nonresponse in Surveys. New York, NY: Wiley.
43. Salthouse, T. A., Nesselroade, J. R., and Berish, D. E. (2006). Short-term variability and the calibration of change. J. Gerontol. Psychol. Sci. 61, P144-P151. Available online at: http:www.ncbi.nlm.nih.gov/pmc/articles/PMC3838959/?report=reader
44. Schmiedek, F., Hildebrandt, A., Lövden, M., Wilhelm, O., and Lindenberger, U. (2009). Complex span versus updating tasks of working memory: the gap is not that deep. J. Exp. Psychol. Learn. Mem. Cogn. 35, 1089-1096. doi: 10.1037/a0015730
45. Schumaker, L. L. (2007). Spline Functions: Basic Theory, 3rd Edn. Cambridge: Cambridge University Press.
46. Smith, L. B., and Thelen, E. (2003). Development as a dynamic system. Trends Cogn. Sci. 7, 343-348. doi: 10.1016/S1364-6613(03)00156-6
47. Soong, T. T. (1973). Random Differential Equations in Science and Engineering. New York, NY: Academic Press 113-135.
48. Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. (2003). WinBUGS Manual [version 1.4.1]. Cambridge: MRC Biostatistics Unit; Cambridge University. (Accessed November 1, 2010).
49. Steele, J. S., and Ferrer, E. (2011). Latent differential equation modeling of self-regulatory and coregulatory affective processes. Multivar. Behav. Res. 46, 956-984. doi: 10.1080/00273171.2011.625305
50. Voelkle, M. C., and Oud, J. H. L. (2013). Continuous time modeling with individually varying time intervals for oscillating and nonoscillating processes. Br. J. Math. Stat. Psychol. 66, 103-126. doi: 10.1111/j.2044-8317.2012.02043.x
51. Von Oertzen, T. V., and Boker, S. M. (2010). Time delay embedding increases estimation precision of models of intraindividual variability. Psychometrika 75, 158-175. doi: 10.1007/s11336-009-9137-9
52. Wahba, G. (1990). Spline Models for Observational Data. Philadelphia, PA: Society for Industrial and Applied Mathematics.
53. Wang, L., Hamaker, E., and Bergeman, C. S. (2012). Investigating inter-individual differences in short-term intra-individual variability. Psychol. Methods 17, 567-581. doi: 10.1037/a0029317