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Nonlinear Regression Equations
Nonlinear regression analysis and its applications. Crainiceanu, C. Likelihood ratio tests for goodness-of-fit of a nonlinear regression model. Journal of Multivariate Analysis, 91 1 , Fujii, T. Nonlinear regression modeling via regularized wavelets and smoothing parameter selection. Journal of Multivariate Analysis, 97 9 , Gross, A.
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The correction for restriction of range and nonlinear regressions: An analytic study. Applied Psychological Measurement, 11 2 , Hanson, S. Huet, S. New York: Springer. McGwin, G. Using nonlinear regression to estimate parameters of dark adaptation.
Linear Regression Equations
Rao, B. Estimation of cusp in nonregular nonlinear regression models. The Nonlinear platform also provides predefined models, such as polynomial, logistic, Gompertz, exponential, peak, and pharmacokinetic models. See the Fit Curve topic for more information.
Nonlinear Regression | Wiley Series in Probability and Statistics
Note: Some models are linear in the parameters for example, a quadratic or other polynomial or can be transformed to be such for example, when you use a log transformation of x. Example of Fitting a Custom Model. Launch the Nonlinear Platform. The Nonlinear Fit Report. Nonlinear Platform Options.
For moderately nonlinear models, the program will find the best parameter values even though the initial estimates may be poor. For highly nonlinear models, good initial estimates are required. Initial estimates should always be realistic for the physical phenomena that are being described. It is very important that the calculated model values for the data set using the initial estimates are reasonable and of the same order of magnitude when compared to the dependent variable values in the data set.
- Describe nonlinear relationships and make predictions from experimental data.
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For difficult situations, it may be useful to linearize or simplify the model and use the multiple linear regression option to determine parameter values that can then be used as the initial estimates for the nonlinear regression. See the following section for a detailed discussion of techniques for linearization of nonlinear models. The program uses the Levenberg-Marquardt LM algorithm as the default for finding the parameter values.
The objective function that is minimized is the ithe sum of squares of the errors. The error is the difference between the actual value of the dependent variable and the calculated value of the dependent variable from the model expression. A detailed explanation of this method can be found, for example, in the book by Press et al.
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Two different implementations of the LM method are included. The LM technique is an iterative solution method that usually converges very rapidly, except when the Hessian matrix becomes nearly singular. In such cases, the algorithm switches to the steepest descent method, the convergence of which can be very slow. A nearly singular Hessian matrix often indicates that there are more parameters in the model than are justified by the data.