Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher
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| Title: | Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher |
|---|---|
| Language: | English |
| Authors: | Deboeck, Pascal R. |
| Source: | Multivariate Behavioral Research. 2010 45(4):725-745. |
| Availability: | 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 |
| Peer Reviewed: | Y |
| Page Count: | 21 |
| Publication Date: | 2010 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Computation, Calculus, Statistical Analysis, Statistical Bias, Correlation, Death, Diseases, Change, Time, Models, Foreign Countries |
| Geographic Terms: | United Kingdom |
| DOI: | 10.1080/00273171.2010.498294 |
| ISSN: | 0027-3171 |
| 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.) |
| Abstractor: | As Provided |
| Number of References: | 19 |
| Entry Date: | 2010 |
| Accession Number: | EJ895134 |
| Database: | ERIC |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/00273171.2010.498294 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 21 StartPage: 725 Subjects: – SubjectFull: Computation Type: general – SubjectFull: Calculus Type: general – SubjectFull: Statistical Analysis Type: general – SubjectFull: Statistical Bias Type: general – SubjectFull: Correlation Type: general – SubjectFull: Death Type: general – SubjectFull: Diseases Type: general – SubjectFull: Change Type: general – SubjectFull: Time Type: general – SubjectFull: Models Type: general – SubjectFull: Foreign Countries Type: general – SubjectFull: United Kingdom Type: general Titles: – TitleFull: Estimating Dynamical Systems: Derivative Estimation Hints from Sir Ronald A. Fisher Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Deboeck, Pascal R. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2010 Identifiers: – Type: issn-print Value: 0027-3171 Numbering: – Type: volume Value: 45 – Type: issue Value: 4 Titles: – TitleFull: Multivariate Behavioral Research Type: main |
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