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Non-Linear Regression

Non-Linear Regression

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Non-Linear Regression

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  1. Non-Linear Regression • What is it? • Why and when to use? • Model assumptions • Typical non-linear models • Obtaining parameter estimates AGR206

  2. Non-linear regression • What is it? • Model is non-linear in the parameters. • Types of models: • Linear. • Intrinsically linear. • Intrinsically non-linear. • Non-linear regression minimizes SSE numerically, by trying many values of the parameter estimates. • Properties of parameters and predictions cannot be derived with equations. AGR206

  3. When and why to use? • Function relating Y to X's is known on the basis of a mechanistic understanding of the process. • For example, the logistic growth model is based on the fact that for some populations, individuals compete for resources and reduce each other's growth rate linearly as density increases. • Parameters of the model have a direct biological meaning. The model may offer the only way to empirically estimate the value of the parameter. • In the previous example, the parameters of the logistic equations are the intrinsic relative growth rate (r) and carrying capacity (K). • Nonlinear models may characterize responses better with fewer parameters than linear ones, even when no apriori functional form is available. AGR206

  4. Exponential growth AGR206

  5. Two-term exponential AGR206

  6. Mitscherlich’s response AGR206

  7. Mitscherlich graph AGR206

  8. Michaelis-Menten AGR206

  9. Segmented Model AGR206