Applications of Nonlinear Models. AIR 1984 Annual Forum Paper.
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| Title: | Applications of Nonlinear Models. AIR 1984 Annual Forum Paper. |
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| Language: | English |
| Authors: | Stewart, Ian, Johnson, F. Craig |
| Peer Reviewed: | N |
| Page Count: | 31 |
| Publication Date: | 1984 |
| Document Type: | Opinion Papers Speeches/Meeting Papers |
| Descriptors: | College Administration, Equations (Mathematics), Estimation (Mathematics), Higher Education, Institutional Research, Mathematical Models, Maximum Likelihood Statistics, Prediction, Statistical Studies |
| Abstract: | Some of the conceptual qualitative ideas needed to test nonlinear models empirically and to modify them are described. Relationships among these ideas and computer applications are also examined to elucidate the general process of nonlinear modeling. Two examples are presented along with a discussion of bifurcation, catastrophe, and maximum likelihood estimate methods. The first example concerns administrators' responses to innovation and uses a verbal description of events. The model is developed based on variables such as the amount of voluntary effort committed to the innovative project and the level of funding agreed to by the institution. An equation consistent with the hypotheses is presented. The second example starts with a mathematical model of promotions within an organization and shows how to go beyond the verbal statements. It is concluded that many observed phenomena in institutions are suggestive of nonlinear dynamics models. A number of standard types of dynamic behavior are well understood mathematics (catastrophe, periodicity, stochastic effects) and may be used to construct plausible models. (Author/SW) |
| Entry Date: | 1984 |
| Accession Number: | ED246763 |
| Database: | ERIC |
| Abstract: | Some of the conceptual qualitative ideas needed to test nonlinear models empirically and to modify them are described. Relationships among these ideas and computer applications are also examined to elucidate the general process of nonlinear modeling. Two examples are presented along with a discussion of bifurcation, catastrophe, and maximum likelihood estimate methods. The first example concerns administrators' responses to innovation and uses a verbal description of events. The model is developed based on variables such as the amount of voluntary effort committed to the innovative project and the level of funding agreed to by the institution. An equation consistent with the hypotheses is presented. The second example starts with a mathematical model of promotions within an organization and shows how to go beyond the verbal statements. It is concluded that many observed phenomena in institutions are suggestive of nonlinear dynamics models. A number of standard types of dynamic behavior are well understood mathematics (catastrophe, periodicity, stochastic effects) and may be used to construct plausible models. (Author/SW) |
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