Non-Linear Regression What is it? Why and when to use? Model assumptions Typical non-linear models Obtaining parameter estimates 7-Apr-19 AGR206

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. 7-Apr-19 AGR206

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. 7-Apr-19 AGR206

Exponential growth 7-Apr-19 AGR206

Two-term exponential 7-Apr-19 AGR206

Mitscherlich’s response 7-Apr-19 AGR206

Mitscherlich graph 7-Apr-19 AGR206

Michaelis-Menten 7-Apr-19 AGR206

Segmented Model 7-Apr-19 AGR206