Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher

Autor/in	Deboeck, Pascal R.
Titel	Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher
Quelle	In: Multivariate Behavioral Research, 45 (2010) 4, S.725-745 (21 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0027-3171
Schlagwörter	Computation; Calculus; Statistical Analysis; Statistical Bias; Correlation; Death; Diseases; Change; Time; Models; Foreign Countries; United Kingdom + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Statistische Analyse; Korrelation; Sterbefall; Tod; Todesfall; Disease; Krankheit; Wandel; Zeit; Analogiemodell; Ausland; Großbritannien
Abstract	The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided. (Contains 3 figures, 4 tables, and 1 footnote.) (As Provided).
Anmerkungen	Psychology Press. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10