Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

REFERENCES

• Bisconti , T. L. , Bergeman , C. S. and Boker , S. M. 2004 . Emotional well-being in recently bereaved widows: A dynamical systems approach . The Journals of Gerontology Series B: Psychological Sciences and Social Sciences , 59 : 158 – 167 .
   PubMed Web of Science ®Google Scholar
• 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 . Psychology and Aging , 21 ( 3 ) : 590 – 599 .
   PubMed Web of Science ®Google Scholar
• Boker , S. M. 1998 . Age-based comparisons of nonlinear dependency in postural control , Philadelphia : Annual Meeting of the Gerontological Society .
   Google Scholar
• Boker , S. M. 2001 . “ Differential structural equation modeling of intraindividual variability ” . In New methods for the analysis of change , Edited by: Collins , L. M. and Sayer , A. G. 5 – 27 . Washington , DC : American Psychological Association .
   Google Scholar
• Boker , S. M. and Bisconti , T. L. 2005 . “ Dynamical systems modeling in aging research ” . In Quantitative methods in aging research , Edited by: Boker , S. M. and Bergeman , C. S. Mahwah , NJ : Erlbaum .
   Google Scholar
• Boker , S. M. and Covey , E. S. 2002 . Two recent advances in estimating and testing differential equations models . Society of Multivariate Experimental Psychology , October
   Google Scholar
• Boker , S. M. , Covey , E. S. , Tiberio , S. S. and Deboeck , P. R. 2005 . “ Synchronization in dancing is not winner–takes–all: Ambiguity persists in spatiotemporal symmetry between dancers ” . In North American Association for Computational, Social, and Organizational Science Available online at http://www.casos.cs.cmu.edu/events/conferences/2005/conference_papers.php
   Google Scholar
• Boker , S. M. and Ghisletta , P. 2001 . Random coefficients model for control parameters in dynamical systems . Multilevel Modelling Newsletter , 13 ( 1 ) : 10 – 17 .
   Google Scholar
• Boker , S. M. and Graham , J. 1998 . A dynamical systems analysis of adolescent substance abuse . Multivariate Behavioral Research , 33 ( 4 ) : 479 – 507 .
   PubMed Web of Science ®Google Scholar
• Boker , S. M. and Laurenceau , J. P. 2005 . “ Dynamical systems modeling: An application to the regulation of intimacy and disclosure in marriage ” . In Models for intensive longitudinal data , Edited by: Walls , T. A. and Schafer , J. L. 195 – 218 . Oxford , , UK : Oxford University Press .
   Google Scholar
• 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 , Edited by: Montfort , K. V. , Oud , J. and Satorra , A. 151 – 174 . Amsterdam : Kluwer .
   Google Scholar
• 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 . Multivariate Behavioral Research , 37 ( 1 ) : 127 – 160 .
   PubMed Web of Science ®Google Scholar
• Deboeck , P. D. 2005 . Using surrogate data analysis to estimate τ for local linear approximation of damped linear oscillators , Notre Dame , IN : University of Notre Dame . Unpublished master's thesis
   Google Scholar
• Duncan , T. E. , Duncan , S. C. , Strycker , L. A. , Li , F. and Alpert , A. 1999 . An introduction to latent variable growth curve modeling: Concepts, issues, and applications , Mahwah , NJ : Erlbaum .
   Google Scholar
• Edgington , E. S. 1995 . Randomization tests, , 3rd ed. , New York : Marcel Dekker .
   Google Scholar
• Emmerich , W. 1968 . Personality development and concepts of structure . Child Development , 39 : 671 – 690 .
   PubMed Web of Science ®Google Scholar
• Gasquet , C. and Witomski , P. 1999 . Fourier analysis and applications: Filtering, numerical computation, wavelets , New York : Springer .
   Google Scholar
• Gottman , J. M. 1981 . Time-series analysis: A comprehensive introduction for social scientists , New York : Cambridge University Press .
   Google Scholar
• Kaplan , D. and Glass , L. 1995 . Understanding nonlinear dynamics , New York : Springer .
   Google Scholar
• Mathematica . 2005 . Computer software , Champaign , IL : Wolfram Research . Website: http://www.wolfram.com
   Google Scholar
• 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 .
   Google Scholar
• Nesselroade , J. R. 1991 . “ Interindividual differences in intraindividual change ” . In Best methods for the analysis of change , Edited by: Collins , L. M. and Horn , J. L. 92 – 105 . Washington , DC : American Psychological Association .
   Google Scholar
• Nesselroade , J. R. and Boker , S. M. 1994 . “ Assessing constancy and change ” . In Can personality change? , Edited by: Heatherton , T. F. and Weinberger , J. L. 121 – 147 . Washington , DC : American Psychological Association .
   Google Scholar
• Nesselroade , J. R. and 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 .
   Google Scholar
• Oud , J. H. and Jansen , R. A. 2000 . Continuous time state space modeling of panel data by means of sem . Psychometrika , 65 : 199 – 215 .
   Web of Science ®Google Scholar
• Polikar , R. October 2004 . The engineer's ultimate guide to wavelet analysis: The wavelet tutorial October , Available from http://users.rowan.edu/polikar/WAVELETS/WTtutorial.html
   Google Scholar
• R. April 2005 . Computer software April , Available from http://www.r-project.org
   Google Scholar
• Ramsay , J. , Hooker , G. , Campbell , D. and Cao , J. 2007 . Parameter estimation for differential equations: A generalized smoothing approach . Journal of the Royal Statistical Society , 69 : 741 – 770 .
   Google Scholar
• Ramsay , J. and Silverman , B. W. 2005 . Functional data analysis , New York : Springer .
   Google Scholar
• Raudenbush , S. and Bryk , A. S. 2001 . Hierarchical linear models: Applications and data analysis methods, , 2nd ed. , Newbury Park , CA : Sage .
   Google Scholar
• Rodgers , J. L. 1999 . The bootstrap, the jackknife, and the randomization test: A sampling taxonomy . Multivariate Behavioral Research , 34 ( 4 ) : 441 – 456 .
   PubMed Web of Science ®Google Scholar
• Schreiber , T. and Schmitz , A. 2000 . Surrogate time series . Physica D , 142 : 346 – 382 .
   Web of Science ®Google Scholar
• Theiler , J. , Eubank , S. , Longtin , A. , Galdrikian , B. and Farmer , J. D. 1992 . Testing for nonlinearity in time series: The method of surrogate data . Physica D , 58 : 77 – 94 .
   Web of Science ®Google Scholar
• Watson , D. , Clark , L. A. and Tellegan , A. 1988 . Development and validation of brief measures of positive and negative affect: The PANAS scales . Journal of Personality and Social Psychology , 54 : 1063 – 1070 .
   PubMed Web of Science ®Google Scholar