Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.
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Boker, S.M., Covey, E.S., Tiberio, S.S., & Deboeck, P.R. (2005). Synchronization in dancing is not winner–takes–all: ambiguity persists in spatiotemporal symmetry between dancers. In 2005 proceedings of the North American association for computational, social, and organizational science.
Boker, S.M., & Kubovy, M. (1998). The perception of segmentation in sequences: local information provides the building blocks for global structure. In Rosenbaum, D.A., & Collyer, C.E. (Eds.) Timing of behavior: neural, computational, and psychological perspectives (pp. 109–123). Cambridge: MIT Press.
Boker, S.M., Neale, M.C., & Rausch, J.R. (2004). Latent differential equation modeling with multivariate multi-occasion indicators. In Montfort, K.V., Oud, J., & Satorra, A. (Eds.) Recent developments on structural equation models: theory and applications (pp. 151–174). Amsterdam: Kluwer Academic.
Boker, S.M., & 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. Multivariate Behavioral Research, 37(1), 127–160.
Broyden, C.G. (1970). The convergence of a class of double-rank minimization algorithms 2. The new algorithm. Journal of the Institute for Mathematics and Applications, 6, 222–231.
Esposito, W.R., & Floudas, C.A. (2000). Deterministic global optimization in nonlinear optimal control problems. Journal of Global Optimization, 17, 97–126.
Fletcher, R. (1970). A new approach to variable metric algorithms. Computer Journal, 13, 317–322.
Goldfarb, D. (1970). A family of variable-metric methods derived by variational means. Mathematics of Computation, 24, 23–26.
Mathematica (2005). Software. Wolfram Research.
Molenaar, P.C. (2004). A manifesto on psychology as idiographic science: bringing the person back into scientific psychology, this time forever. Measurement, 2(4), 201–218.
Nesselroade, J.R., & Ram, N. (2004). Studying intraindividual variability: what we have learned that will help us understand lives in context. Research in Human Development, 1(1–2), 9–29.
R (2007, April). Software. http://www.r-project.org/.
Ramsay, J.O., Hooker, G., Campbell, D. & Cao, J. (2007). Parameter estimation for differential equations: a generalized smoothing approach. Journal of the Royal Statistical Society B, 69, 714–796.
Ramsay, J.O., & Silverman, B.W. (2005). Functional data analysis. New York: Springer.
Shanno, D.F. (1970). Conditioning of quasi-newton methods for function minimization. Mathematics of Computation, 24, 647–656.
Shannon, C.E. A mathematical theory of communication, Bell Systems Technical Journal 27, 379–423, 623–656 (1948).
Takens, F. (1981). Detecting strange attractors in turbulence. In Rand, D.A., & Young, L.S. (Eds.) Lecture notes in mathematics : Vol. 898. Dynamical systems and turbulence. Berlin: Springer.
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Deboeck, P.R., Boker, S.M. Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices. Psychometrika 75, 420–437 (2010). https://doi.org/10.1007/s11336-010-9168-2
- intraindividual variability
- differential equation model(s)(ing)
- time series
- damped linear oscillator
- analytic solution(s)